What single word could be used in place of "long drawn out procedure"?

You might consider drudgery for this.

It's not an exact fit, but it has the right connotation, given its meaning:

From Oxford:

drudgery
noun [mass noun]

Hard menial or dull work.

It is possible for work to be hard and/or dull due to its length and not its actual difficulty. Therefore, a meeting could be a drudgery, or the contents of it can be a drudgery, if the meeting draws out long. The word fits in your sentence as well:

Please people, we need to keep moving if we want to complete the drudgery of this meeting.

I would call those tasks functions. (Wiktionary) (Merriam-Webster)

The singular "function" being:

A relation where one thing is dependent on another for its existence, value, or significance.

and

Any of a group of related actions contributing to a larger action.

Objectives. Or Details. Or both 'detailed objectives'.

'Objectives' means 'all the tasks that have been identified, that need to be done'. And it also means 'the desired results'.

This term is commonly used in business to mean 'all the many and various detailed little things that have to be done' such as filing reports, doing admin, completing procedures, designing something new etc. - it can mean literally anything 'that you are trying to do'.

And in a larger context 'the main objectives' are the bigger goals that are to be achieved - that the 'detailed objectives'- ideally - support. They are 'the object' of the goal - what one is aiming for.

'Details' is another word you could use, that means 'all the complicated little bits and pieces'. All the 'little parts of the whole ' - the whole being the 'main objective'.

https://www.merriam-webster.com/dictionary/detail

The good thing about using 'objectives' in the examples you give, is that 'objectives' is a word that intrinsically focuses on 'the goal' - the 'object' - of what is to be achieved - as well as encompassing the meaning of 'all the little details that have to be done':

• 'we want to keep moving, to achieve the objectives of this meeting'

...means 'the details' and 'the main goal' or goals.

In that way, when you use the word 'objectives' you are also telling people to 'focus on the goal' which is good, because sometimes the focus on the goal is forgotten as people get lost in 'all the little things that (might!) have to be done' - and forget about the main goal.

http://www.businessdictionary.com/definition/objective.html

Example of 'objectives' in a different context - learning https://www.cmu.edu/teaching/designteach/design/learningobjectives.html

Examples:

• we want to keep moving, to complete the objectives of this meeting

• to complete an operation, many objectives must be completed including induction, preparation, the procedure, and close. Within each category are many more detailed objectives that must be completed for each phase to be a success.

• you need to complete these 500 or so objectives to open your store. We suggest you break the objectives into 3 sets of achievable 'objective chunks' like this...

• The main objective is to open your store. Here's a list of 500 detailed objectives, to achieve that.

If you really want the procedure to be 'long and drawn out' then I would not use 'objectives'. I would use 'administration' or a word that focuses less on 'the actual goal' - and more on 'all the little details that have to be done.

• Please people, we need to keep moving if we want to complete the process of this meeting.
• Please people, we need to keep moving if we want to complete the progress of this meeting.

A routine describes

A set of customary or unchanging and often mechanically performed activities or procedures: a routine of housekeeping

So your sentence would be:

Please people, we need to keep moving if we want to complete the routine of this meeting.

If it's an especially laborious process, you can describe it as a grind:

Please people, we need to keep moving if we want to complete the grind of this meeting.

Agonising procedure or process

You can say 'agonising procedure' or 'agonising process' for something long drawn out and... unbearable, or the 'agonising' can mean 'poring over the little details endlessly'.

Agonising is 'causing great physical or mental pain'. It also carries the meaning 'not being able to choose' - 'agonising' can be used alone to mean 'poring over one's choices'.

https://en.oxforddictionaries.com/definition/agonizing

Example:

• the agonising process of identifying the victims from all the remains continues after the air crash tragedy
• going through the agonising process of arranging all the new products in the shop and labelling them all with the correct prices and code numbers

https://www.mirror.co.uk/news/uk-news/agonising-process-identifying-grenfell-tower-10634517

Note, agonising is English, agonizing is American spelling.

Folderol:

Unnecessary actions or words that have little meaning and make something seem more important or complicated than it really is: Unanimous consent simply means the bill passes without all the usual Senate procedural folderol. The first act of the play is full of fussy folderol; the second moves much faster and smoother. Cambridge.org