If you're looking for a system I can recommend Akers' Comrades with some caveats.

It's a bit rules light and you need a party that's confident making decisions with a little scaffolding more than strict limits, which might make it tough for some who are new to TT.

It also sometimes feels like it wasn't all playtested. You may need to adapt some rules on the fly because there are little gaps occasionally, things like that.

But that said, you can have characters drop in and out for most missions because you're playing a cadre so no one is indispensable, and it's setting agnostic. My group is doing a WWI era lord of the rings situation where they simultaneously want to overthrow the dark lord and not fall prey to the "good guys" who want to eradicate everyone else. It comes with suggested settings too if homebrewing is too much work.

I can't necessarily commit to more right now but I will be keeping eyes on your project as it goes, maybe I can join you folks later.

EDIT: For an idea of how it works you could check out Red Game Table/Matryoshka, they are running a different iteration of the same overarching system, both are 'Powered by the Apocalypse' games.