I'd advise for going with the approach of everyone being one ship. Yeah you lose diversity on potential factions and whatnot by not letting everyone be a captain, but FTL has a focus on crewmembers to micromanage at stations and handling that in textual form sounds like a pain in the ass.

Also I don't like it on the basis that it'll end up having players talking to themselves as they'll be controlling however many dudes are on their ship.

As for a premise I don't got one other than pointing out the obvious, that if you're gonna go with the game's plot that you'll need to keep players from dawdling because of that urgency and needing to flesh out encounters more and trying to thread a plot. Because the game's cycle is pretty much combat encounters,warping into hazards, non-combat encounters with some choices, and a shop to resupply & repair every so often.

Also if you're gonna do some sort tabletop system I say use Lasers and Feelings. I don't think you're gonna get a whole lot of people who want to play with the minutiae of various ship systems.