[GM HELP] Need Help with a Mutiny Encounter (Stowaway on the Singing Sea)

[Applied_People]

Not a new GM, but this is my first time running an encounter like this. Potential players of Adventure-a-Week's "Stowaway on the Singing Sea Mini-Dungeon" be warned, SPOILERS BELOW!

Adventure Synopsis:

The basic gist of the adventure is that the players are stowaways aboard a ship that is suspected of piracy. They have been tasked with catching the captain and crew in an act of piracy and have been deputized to arrest the captain (and to offer amnesty for past crimes and 100 gp per crew member who side with the PCs and aid in the capture of the captain. There are 40 crew members in addition to the captain and her first mate. The ship has a large cargo hold (where the PCs are hiding) and is 130 ft long with a 50 ft beam (width at widest point). 

Mutiny Encounter:

When the PCs confront the captain, the encounter is supposed to go something like this:

1) No matter what the PCs do, 10 crew members side with the captain (though they pretend to side with the PCs at first)
2) No matter what the PCs do, 10 crew members side with them
3) The remaining 20 crew members can be persuaded to side with the PCs on a successful DC 25 Diplomacy check.
4) Presumably, a melee will ensue shortly after the PCs confront the captain and make their offer of amnesty to the crew.

Here's where I'm struggling:

1) unless the PCs ask the crew members to physically move to one side of the ship or the other to indicate their "allegiance" or raise hands or something (all of which seems silly), they will have no way of knowing who is on their side and who is against them. I LOVE this, but I don't know how to manage it. Similarly, the captain and first mate won't know...and the crew members themselves won't know. What can I do with this? I'd like to keep this feeling of not knowing who is for you and against you but 

2) With a total of 46 combatants (40 crew, 4 PCs, first mate, and captain), I think the best way to run the combat is to form the crew into troops and use those mechanics to speed up the combat. But I'm open to other ideas. And should they fall out of troops and play as individuals if enough combatants are killed?

So, any and all suggestions welcome. Bonus points if you've run this adventure and can tell me what you did!

Thanks!