You need a new conflict resolution tool

Your question boils down to something buried late in the text of the question.

The fact that we quickly ended up is a 4 hour conversation about a different conflict between the GM and the player in question related to a different past fiat from a previous session may have had something to do with that, however.

Before you play again, you need to bring up this point exactly as you have written it here. You then ask the rest of the players and the GM this question:

"Are we here to play, or are we here to argue?"

Poll the players.

If you get more votes to argue than play, then I suggest you change games.
If you get more votes to play, then write down in large letters on a piece of cardboard

We are here to play, not to argue.

Rules of Engagement that go with this sign

Anyone can raise that sign from the little stand that it sits in, next to the gaming table, when an argument begins such as you have described. Better sooner than later.

I kid you not, I had a DM who had a sign like that back in the early 80's. He would occasionally raise it. That visual cue was profound. It was a great way to get us all to take a breath, and get back to playing.

I have been in a number of games where there was no sign, but one of the players, or the GM, said that exact thing as an argument heated up: "Hey, are we here to play, or are we here to argue?" (Granted, sometimes that was accompanied by "If we don't get back to playing, good night!" as a warning that someone had had enough of this no value added behavior).

• I've run into this with board games and card games as well when people disagree on house rules that arrive in the middle of play. My mother in law is famous for pulling that stunt. It has happend on more than one occasion that someone at the table gets up and says something like "when you are done arguing, let me know, I came here to play" ...

Beyond that, please take a look at my suggested conflict resolution tool. Present it to your table. See if they'd like to try it. If they do, use it. Or, if you think that one's a bit too unwieldy, present the shorter version that @anaximander suggested to me in that question and answer. This tool presumes the GM/Player relationship that Steve Jessop explains in detail, and it goes like this:

"If we disagree, you have three minutes to either find the rule in the book/manual, or convince me {us} it should work how you want. After that I'll make a ruling and tell you why I think it should be that way. There will be no further discussion, and the rule will work that way for the remainder of the session. After the session I will have a more thorough read of the rules, and if you're still unhappy we can discuss further. At the start of next session, I will announce a better-thought-out rule, which we will use from then on, unless we find flaws in it."

Anaximander said that it worked for him at his tables, and I believe him. Again, present this to your table under the basic premise of "we are here to play all night, not argue all night." Any such tool does need buy in from the table.

If what you (collectively) are doing isn't working, change what you are doing.

If you are going to argue "wait, that's GM fiat!" I answer: you have a GM, per your detailed question. If you have deep aversion to GM fiat (remember, a GM/DM was originally called a Judge or a Referee) then play a GMless game. Granted, with this group that you are complaining about, I'll take fifty bucks to Vegas and bet the over on "you'll still argue." And probably win.

While we are looking at this through the lens of your group having some dysfunctional habits, take another look at indigochild's answer. That one struck a chord with me.

Your drastic option is to record each session ...

... and play back the section in dispute where differences arise.
That would surely allow you to get at "the truth of the matter" but ... do you really want to do that?

Do the rest of the people at your table want to do that?

If the answer to those two questions is "Yes!" then do it: record the sessions.
{Heck, now that I think of it, you could post the sessions on youtube ... and turn dysfunction into profit. 8^D }

The group I play with used to have problems that resemble this, and I think a lot of the issue is that you're asking slightly the wrong question. Specifically, it looks to me like your group gets into a situation where you know what the current situation is, but not how you got there; the argument is high stakes because you're having arguments about what happened in the past because it's really a proxy argument about what the current situation means.

In your example, you all agree on what the PC said; what you're really arguing about is whether the NPC ought to be insulted.

And the reason it's really hard to resolve is that you're treating actions and reasons as severable: players are saying "the reason my character did X was because I thought Y", and your group is committed to saying that they definitely did X, even if Y wasn't true. The problem with settling facts without regard to motives is that it leaves players feeling like their character's integrity was violated: they wouldn't have done X without Y, and now they're left with a character who apparently did it anyway.

What worked for us was recognizing that they're not severable: if someone did X because of Y, and your group clarifies that actually Y isn't true, it also follows that the character didn't do X.

There are two techniques that helped us that might help you:

1. Recognizing that the important thing is finding a shared consensus, not the true story of what happened. Ignore the question of what actually happened; have everyone go around and explain what they think happened and why. Then ask: what does everyone need to be true. Does it matter that that the other PCs weren't talking, or could you rewrite the history so that they were talking? Could the PC have insulted the NPC, even if that's not what the player was expecting? Put aside entirely the question of what actually happened; here are a lot of reasons people fall out of sync about that (people misunderstand, they mishear, they get distracted, they forget things). Litigating what actually happened isn't important; having a mutually acceptable situation going forward is.

2. Being prepared to modify what happened ("Okay, my PC wasn't talking, but sure, we can decide that actually she was in the middle of saying something") or, if necessary, backtrack: "My PC wouldn't have said that if the NPC wasn't talking over people, so let's back up to when the NPC started talking and take it from there". It took some practice for us, but we got better over time at finding ways to salvage content: at saying "I really liked what happened when it seemed like you insulted the NPC; is there something that could have happened that makes sense for your character, but still makes that happen?"

The GM Reminds Everyone Of Reality Immediately

If players seem to be confused about something their characters should know, it's the GM's job to step in and remind everyone of what the characters know.

The GM should do this as soon as the confusion becomes apparent, so as to prevent the players from wasting time thinking about a game world that they're not actually playing in.

If a player notices that players seem to be confused about what their characters know, but the GM hasn't stepped in and reminded everyone what their characters know, the player should turn to the GM and ask them to deliver that reminder.

In games that I run, it's uncommon for a player to be that confused about what their character would know. But when it does happen, I follow these instructions to get the group un-confused, and then we move on with the game.

An RPG requires a consensual fiction. Usually nobody has perfect recall, but it must be at least consensual enough that you can proceed.

So, to review what I'm sure you already know: the "traditional" way of establishing that consensual reality is that the GM is the arbiter of what has happened in the game fiction. The GM accepts players' descriptions of their own characters' actions as they occur. Players accept the GM's narration of everything else, including the outcomes of PC actions. In cases where a player cannot remember, or there is dispute, players appeal to the GM, saying, "what actually happened?". In cases where the GM cannot remember, they might then ask the players to help to reconstruct events.

In cases where one or more players really think the GM is wrong then there might be some discussion, but it is in the nature of trad games that this must be rare, brief, and with a presumption that the GM makes the final call. In cases where a player can no longer in general accept the GM's rulings, they voluntarily stop playing under that GM. Players offer or refuse consensus by participating in the game or not participating. They do not offer or refuse consent to each in-game event separately (except where you have mechanisms in place like lines/veils, where players do not consent to particular content).

Clearly what's happening in your games is not of this nature.

There are exceptions to this basic procedure. For example, a player's description is usually not binding in cases where they've misheard the GM and quickly want to take it back (you may or may not call this a retcon, depending how quickly it happens and how annoyed you are by the situation). Depending on the GM (and any discussions among the group), players might get more or less leeway for less direct forms of misunderstanding. Or, if the GM wants the PCs to argue, they might say, "well, each character remembers it as the player remembers it: I'm not going to remind you what really happened". This is not the same as the players establishing the game fiction.

Again, clearly this is not all that's happening in your games.

It is quite impossible for it to take 2-6 hours for everyone to have their say how they remember a short series of recent events. Something else is going on during those arguments (repetition, off-topic issues, personal insults, recapitulation of previous arguments, one person flatly refusting to proceed until they get their way, etc). All of those other things need to stop if you are to continue playing the game. I also observe that one person cannot have a 6 hour argument on their own, and you need to honestly check that you are right not to let the odd-one-out have things their way.

Since your group seems guided by formal (albeit as you say not ideal) procedures, rather than a shared expectation of what constitutes good-faith effort to a common purpose, someone (either the GM or the players collectively) needs to draw up a new procedure. I suggest three main changes from the procedure you describe:

• Do not even mention value differences. You are resolving what events took place. Whether those actions were rude or not is for each individual to judge independently[*]. So, "was the NPC insulted?" is not a valid question for discussion. It is a secret about the world, which the GM knows and the players can only speculate about. "Were the other PCs speaking?" is a valid question for discussion. Get rid of the procedure for immaterial differences.
• Drastically reduce the time limit, from 2 hours to at most the time it takes to go around the circle letting everyone speak once, plus any time the GM needs to ask further questions, plus a couple of minutes thinking time.
• Do not require consensus as to what everyone remembers. Use GM fiat more and sooner.

Note that the procedure then does not include general discussion, which must therefore be deferred until after the session (or perhaps during a planned break in the session).

If a player cannot sign up to the procedure for a particular game, and in particular if a player cannot trust the GM's memory sufficiently to accept their version of events in a trad game, then that player cannot play that game. It's never nice to throw someone out of the group, but ultimately, as the last resort, if one person declines to play the game that everyone else is trying to play, then why are they there?

Either get them to agree to play your game, or else play their game, or else play without them. Perhaps by presenting a new procedure which aims to move the game along, they will agree that this is more important than them always getting their way, and you can all play differently in future. Perhaps they will say that they simply cannot proceed with the game if the official version of events does not match their memory, in which case they can leave. But you have to bring them to that decision in order to get the game moving.

Naturally there are reasons non-trad models exist, such as some groups not wanting such a strong authroritarian streak in the GM's role. But it has the virtue of clear responsibilities and fast decision-making, which is why I recommend it for this case.

However, if the reason that you haven't already gravitated towards the model of "just ask the GM what happened" is that you collectively don't want that authoritarian GM role, then you could try other games entirely. Try playing a GM-less game for a session or two and see whether that resolves the conflict. I suspect it probably won't, but if it's the GM role that's the problem (rather than the players who absolutely must get their own way even when in a minority of one) then quite possibly it will.

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[*] I'm assuming here a group where everyone is able to make independent value judgements and to accept that these differ between individuals. Perhaps one or more people in the group can't do that (let's say they don't easily distinguish opinion about social judgements from objective fact, which might perhaps be a symptom of autism or could just be someone's idiosyncrasy; or they don't accept that different people can make legitimate ethical assessments which differ, which might perhaps be a symptom of a hardline ethical position such as utilitarianism or fundamentalist religion; or perhaps they have so little experience of cultures and social classes other than their own, that they struggle to acknowledge even in fiction when unfamiliar rules of etiquette apply). In that case I would still suggest to move to the "GM fiat" model, but extend it to more than just the sequence of events.

Conflicting descriptions of the recent past shouldn't exist. The GM is (or should be) aware of the game's state, and should be consulted when that state is unclear to players

That's a little bit exaggerated, for emphasis, but it's largely true for most tabletop game systems. Players can describe what they do, but until the GM has accepted and processed that information it hasn't happened in the game.

This is usually necessary both because the GM's mind is running the game world (updating the state of things in the game world can only be done by the GM) and also because the game simulates synchronous activity asynchronously (a real conversation doesn't necessarily occur in turn order, or two real conversations can be happening at the same time while the GM can only handle one at any given moment).

These factors mean that the only reliable information on the current situation in-game is in the GM's head, and consequently it is their job to express that information to players clearly. If the GM makes a mistake (a player reminds them that X happened and therefore Y could not be the case, for example) the GM should correct themselves and reiterate the actual state of the game world to players for clarity.

If a player is mistaken and takes an action based on that mistake, they should be corrected (mildly), and then have the opportunity to revisit their recent action in light of what they "should have" (and their character would have) known by being present in the game world.

As a GM, I typically work from the assumption that miscommunications about the state of the game world are my fault. I didn't explain things clearly enough, or phrased something poorly, or emphasized the wrong thing which distracted from a salient point, etc. When there is misunderstanding or mismatched conceptions of a scene in players' minds, the correct information should be reviewed and described to the players. This process usually takes moments, not hours.

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The game's state is not based on a consensus of player opinions

As a logical follow-up to the above, the GM has an important role in tracking the state of the game world. It is important that the GM keep in mind what's important to a scene, as well as where the PCs are and what they have done. At any given moment, the GM should be able to provide a quick summary of the scene's events leading up to the current state, and the current state itself.

Corrections should happen immediately when they apply. Games are much less playable when players don't have correct information on the game world. The example disagreement about players discussing who was speaking and when (the PCs and/or the NPC) is generally not a discussion for players to have. They can discuss their recollections of events, but for matters of fact the right move is to ask the GM.

The GM knows that information (or should), and it's something that the PCs would certainly be aware of and so, if that information is unclear to the players, they should clarify it by checking with the person responsible for knowing the state of all in-game entities. If a player declared an action based on a misunderstanding of the situation, it's often a good idea to let them reconsider based on the accurate information once the misunderstanding is addressed.

If PCs are in a room with a rectangular door, there should never be an argument among the players about what shape the door is-- that's a waste of time. The state is readily discern-able to the PCs, and so querying the GM to see if their (the players') memories are correct is the right way to resolve uncertainty.

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The GM's approach should conform to the players' patterns

If it's a common issue that a player forgets things they've just done ("I open the door" --> "I never opened the door, I wouldn't do that!"), then the GM should impose more structure on their behaviors to address that tendency. This can be as easy as my approach, which is to simply restate what the player declares, asking for additional detail as needed:

Player: I open the door GM: OK, you approach the door. Where are you standing when you start opening it?

It's a lot harder to argue "I never opened the door" after that single sentence. If the problem is specific to some players, it can be a good idea to have their action declarations be more formal. Nothing actually happens in-game until the GM accepts the player's declarations, and once the GM has done so whatever the player declared has happened and is not open to dispute or revision. GMs are variably strict on that sort of thing, but it seems to me that your current GM's approach is engendering significant problems at the table right now and so a bit more strictness might be worth exploring.

You've described a process by which different players make competing claims and the truth of those claims is decided largely through consensus. As you've found, this takes forever and doesn't produce solid results.

Don't decide facts by consensus. Each player (and GM) controls their own actions.

Consensus is a time consuming in imprecise way of determining what is and isn't true. At best, you can create some kind of intersubjective understanding that will get you by - until the next problem arises.

Players can reasonably expect agency over their characters actions. If one of these discussions starts, and a player says that they did or didn't do something - then they did (or didn't) do it.

GMs can reasonably expect agency over their NPCs. If one of these discussions starts, and the GM says that an NPC did or didn't do something - then they did.

Other players opinions are unimportant, because the actions of other players' characters and NPCs is beyond their control. This premise will save you a lot of time and hopefully, help build some respect at the table.

If the disagreement exists between players (not a player and the GM), then it is the GM's role as "referee" to decide what did or didn't occur in-game. Embrace GM fiat - it's the tool designed for exactly this kind of problem.

But that isn't really the problem

Although you've explicitly asked about how to handle a very rational kind of problem, this is basically an XY problem. The problem really lies with how your GM and players perceive their individual roles:

• GMs control the in-game world, except the PCs. They have final say over what happens (and has happened!) in the game world. Players should accept and respect this as a part of agreeing to play at the table.

• Players control their own characters. They have final say over what they do and don't do, subject to the rules of the game. Other players should accept and respect that.

• The GM is a referee for disagreements between players, or between players and the GM. Everyone at the table should accept and respect that. Once the GM has articulated a decision, move on.

Although your decision making process may not be ideal, it's not the core of your problem. You can improve that process, but you can only reduce the symptoms, not eliminate them. The underlying problem is that the people at your table don't appear to be respecting each other's agency and roles, which causes conflict.

The distinction I want to emphasize is that the first section is about the actions that the players and GM can take (declaring what their character has done), while this emphasizes the social culture of your table - their beliefs about what each person at the table should be doing, and what the authority of the GM is. If you can build agreement on those roles and respect each other, then the decision making process will become much easier on its own.

This isn't an RPG problem: it's a human problem

Nobody has a good, let alone perfect, memory.

Hence:

It is characteristic of all committee discussions and decisions that every member has a vivid recollection of them and that every member’s recollection of them differs violently from every other member’s recollection. Consequently, we accept the convention that the official decisions are those and only those which have been officially recorded in the minutes by the officials, from which it emerges with an elegant inevitability that any decision which has been officially reached will have been officially recorded in the minutes by the officials and any decision which is not recorded in the minutes has not been officially reached even if one or more members believe they can recollect it, so in this particular case, if the decision had been officially reached it would have been officially recorded in the minutes by the officials, and it isn’t so it wasn’t.

Sir Humphry, Yes, Prime Minister Season 2, Episode 1 Man Overboard (at 1:07)

So, if it's important, write it down at the time and get everyone to agree to accept the written record.

Trust players to remember their characters' actions honestly

If a player says their character didn't do something then they should be trusted. Sometimes plots get confusing and we think something happened a certain way. When push comes to shove, however, the player is the one that knows best how their character would have acted. Ruling that a character did something that the player doesn't think they did runs into issues of player agency. If a player starts lying about what their character did then you have a different issue that needs to be addressed.

As an example:

Yilun thinks Xaratron stabbed Yilun but Xaratron thinks otherwise.

Yilun: "Xaratron stabbed me"
Xaratron: "No I didn't"
Yilun: "You didn't. I thought you had"
Xaratron: "I didn't. I wouldn't do that."
Yilun: "Okay then."

Because the material question is about Xaratron's actions Xaratron's version of events should be accepted. If this requires Yilun to retcon an action that is better than having Xaratron's player believe their agency was overruled.

If it seems like a player is abusing this trust then there needs to be a conversation about game expectations similar to what you would have if a player was metagaming or fudging rolls. Consider this answer for tips https://rpg.stackexchange.com/a/98316/60913

Treat the Players' different memories as their Characters' different memories

If there is no physical difference in the game between the two memories the you don't need to determine which one is true. Sometimes people misremember and it is impossible to prove what actually happened. What is relevant to the story, however, is what the characters think happened.

As an example:

Stella thinks Yilun's character insulted Xaratron, the NPC, by interrupting Xaratron. Yilun thinks that their character did not interrupt Xaratron.

Stella, Yilun, and the GM will determine each of the characters' memories of the interaction to decide how to respond. The GM does not need to rule that Yilun's character did not interrupt Xaratron only that Xaratron is not angry at Yilun's character.

By moving the issue from a question of "What actually happened?" to "What does my character think happened?" it allows each player to act out their memory of the situation. If Stella's character then tries to persuade Xaratron to turn against Yilun's character and Xaratron refuses it is not necessarily because Stella misremembered the material facts but rather that Stella's character misunderstood the immaterial facts.

Let a player retcon their actions

If Yilun thinks Xaratron stabbed him and so poisons Xaratron's coffee but it is decided that Xaratron did not stab him then you can let Yilun say they did not then poison the coffee.

This works best when it is done quickly rather than later on in the plot so it is worthwhile for players to state their intentions when they take an action. This would go like this

Yilun: "I am angry at Xaratron for stabbing me and so I poison Xaratron's coffee"
Xaratron: "I didn't stab you"
Yilun: "You didn't? I thought you did."
Xaratron: "I didn't."
Yilun: "Okay, then instead I will order my own coffee and sit down"

This reduces the cost to players of having differing understandings of events. Xaratron is happy because they didn't stab Yilun. Yilun is happy because they didn't act based on an incorrect understanding of events.

This can be used with the first method or with GM fiat but either way it can make the transition smoother.