Is the hyphen in the adjective phrase “just-[past participle]” mandatory?

Reduced relative adjective clause:

Reduction: the record type [that was] just mentioned.

Example of a university writing center explaining this:

Reduced Adjective Clauses We reduce sentences when you have the same subject in the main clause and the adjective clause. Adjective clauses contain relative pronouns like who, which, or that. The reduced adjective clause becomes an adjective phrase, which does not have a subject. An adjective phrase does not have a subject and a verb. Instead, it has a present participle (base verb + ing) for the active voice or a past participle for the passive voice. [bolding mine]

Mt. San Antonio College

Grammatically, your sentence is acceptable. You will be using "just mentioned" as an adjectival phrase modifying "record types." The longer alternatives you proposed work, too, but this is a fine construction.

As a matter of punctuation (as opposed to grammar), the Chicago Manual of Style would hyphenate the phrase, following the general rule that hyphens are used to add clarity to phrases that come before the noun they modify. CMoS 16th, §7.79 (regret no link - I'm old school and referred to my hardbound copy!)

Continuing on this punctuation front, hyphens aren't necessary with compounds that include adverbs ending in -ly. And CMoS says you usually won't need the hyphen in a phrase that comes after the noun it modifies.

CMoS is an American authority. I glean from comments that different guidance might apply in other places.

A hyphen is neither obligatory, nor optional, because the question is based on the wrong assumptions. A hyphen, in this case, would be a prime example of overuse, and it would clarify nothing.

So let us be clear, as stated: there are two meanings for the word "just". One meaning is derived from, and related to, "justice". The other is a matter of time: i.e. something of the very recent past.

The question posits that a hyphen should be used for clarity. Indeed, numerous usage guides tell us that hyphens should be used when they clarify meaning. Yet, using a hyphen, in this case, would not clarify WHICH usage pertains.

The questioner wants to regard the 1st dictionary meaning as the dominant meaning, regardless of context, one that should be adhered to unless something clearly indicates otherwise.

With the given sentence, I believe that the first meaning of the word, as an adjective, takes precedence.

This thought is spurious in itself. One needs to first regard context when determining which usage applies, not dictionary order. The context of the sentence clearly provides that the 2nd meaning, of time, is the intended meaning.

So, one must simply apply context as a rule. In the given sentence:

The target can be resolved through one of the just mentioned record types.

does applying the meaning of justice make sense? The answer is obviously no. Therefore, the intended meaning must be that which attributes time. A simple substitution will validate this:

The target can be resolved through one of the recently mentioned record types.

Use of the hyphen in the latter case would be superfluous and would clarify nothing. Therefore, if used, it would be an example of overuse. Even regarding it as optional would seem to indicate that such usage might be acceptable, but I think it clearly is not acceptable form, thus the hyphen is neither obligatory nor optional. See the 2nd case here: https://www.dailywritingtips.com/5-cases-of-extraneous-hyphenation/

Bryan Garner, Garner's Modern American Usage, third edition (2009) includes a lengthy discussion of what Garner calls "phrasal adjectives." The following portions seem relevant to the question posted here:

PHRASAL ADJECTIVES. A. General Rule. When a phrase functions as an adjective preceding the noun it modifies—an increasingly frequent phenomenon in 20th- and 21st-century English—the phrase should ordinarily be hyphenated. Hence the soup is burning hot becomes the burning-hot soup; the child is six years old becomes the six-year-old child. Most professional writers know this; most nonprofessionals don't.

The primary reason for the hyphens is that they prevent miscues and make reading easier and faster. ...

...

Upon encountering a phrasal adjective, the reader isn't misled into thinking momentarily that the modifying phrase is really a noun itself. In other words, the hyphens greatly clarify the meaning. It matters a great deal, for example, where you put hyphens in last known criminal activity report.

Some guides might suggest that you should make a case-by-case decision, based on whether a misreading is likely. You're better off with a flat rule (with a few exceptions noted below) because almost all sentences with unhyphenated phrasal adjectives will be misread by someone.

Applying Garner's analysis to the instance raised in the posted question, we get the record types just mentioned becomes the just-mentioned record types.

Basically, Garner is endorsing reflexive use of hyphens in (most) compound modifiers, rather like reflexively using your turn signal instead of deciding case by case whether the driver of the nearest car behind you is close enough to benefit from your signaling. It is true that some readers may find the inclusion of the hyphen in many such instances excessive or unnecessary—and some may even argue that this makes the punctuation incorrect—but I don't think that anyone can plausibly argue that including the hyphen risks misleading the reader. Opposition to including the hyphen focuses on the idea that it is overkill, not that it produces ambiguity.

The Chicago Manual of Style, sixteenth edition (2010) shows signs of being one of the "guides [that] might suggest that you should make a case-by-case decision" that Garner mentions. Here is its advice on the topic of hyphenating compound modifiers:

7.80 Hyphens and readability. A hyphen can make for easier reading by showing structure and, often, pronunciation. ... Hyphens can also eliminate ambiguity. For example, the hyphen in much-needed clothing shows that the clothing is greatly needed rather than abundant and needed. Where no ambiguity could result, as in public welfare administration or graduate student housing, hyphenation is unnecessary.

On its face, this guideline seems to advise writers to weigh the potential ambiguity of every compound modifier that appears in front of the noun it modifies and to decide on that basis whether to hyphenate the modifier. But two factors muddy the clarity of that advice.

First, the two examples that Chicago provides as instances in which hyphens are unnecessary—public welfare administration and graduate student housing—are not merely unambiguous; they are set phrases. It is one thing to say that "real estate agent" shouldn't be hyphenated (because, in that wording, "real estate" is an instantly recognizable and unitary phrase within a longer set phrase); it is quite another to say that "real estate planning," in the sense of "planning about real estate," shouldn't be hyphenated (because, in that wording, it isn't clear that "real estate"—rather than "estate planning"—is intended as a unitary phrase within the longer phrase "real estate planning," and because that longer phrase isn't a set phrase).

Second, Chicago also provides a detailed chart of specific compound modifiers that it recommends hyphenating, even though leaving some of these compounds unhyphenated would at most slow the reader down momentarily. In none of the following instances in which Chicago recommends using hyphens is the hyphenation necessary to resolve ambiguity: a five-year-old child, reddish-brown flagstone, snow-white dress, a two-thirds majority, a hundred-meter race, a fifty-year project, third-floor apartment, a middle-class neighborhood, a much-needed addition, a too-easy answer, a decision-making body, a clothes-buying grandmother, an over-the-counter drug, an up-to-date solution.

In its introduction to this chart, Chicago includes the following comment:

Chicago prefers a spare hyphenation style: if no suitable example or analogy can be found either in this section [the chart that follows] or in the dictionary, hyphenate only if doing so will aid readability.

But the examples I've cited above suggest that Chicago uses "readability" in a rather plastic way. At what point does leaving the reader free to wander down the wrong garden path become an issue of readability, if we accept that the reader will almost certainly figure out the intended sense of the unhyphenated phrase eventually? If you refer to "a little used car" when you mean "a little-used car," you are in danger of having a significant portion of your readers misapprehend your intended meaning. Relatively few phrases fall into this truly problematic category; nevertheless, one of the hidden advantages of hyphenating heavily (after the Garner method) rather than lightly (à la Chicago) is that when a potentially ambiguous sentence does arise, you have given your readers confidence that the absence of punctuation is an intentional signal of how the sentence should be interpreted: "a little used car" really is a small car that is no longer new.

To judge from the coverage of compound modifiers and hyphenation in The Oxford Guide to Style (2002), British style is more strongly inclined than U.S. style is to hyphenate such compounds when they appear before the noun that they modify. Here is the relevant guideline from Oxford:

Hyphenate two or more modifiers preceding the noun when they form a unit modifying the noun:

[Examples:] a stainless-steel table, the blood-red hand, the well-drawn outline, the up-to-date records, a long-standing agreement, honey-blonde curls

Some of these instances are arguably necessary to cure lurking ambiguity. (Oxford points out, for example, that "A stainless steel table is a clean table made of steel, while a stainless-steel table is a table made of stainless steel.") But in general Oxford seems far less interested in ferreting out possible ambiguity than in using the hyphen to signal the unity of the modifying phrase. In this respect, Oxford seems much more aligned with Garner than with Chicago.

Ultimately, whether "just mentioned record types" should be hyphenated as "just-mentioned record types" is a style question, not a matter of grammar. Different writers and different publishing houses follow different guidelines that are based on different preferences. All of us might agree that some punctuation styles are better than others, but I seriously doubt that all of us can agree on which ones those better ones are.