The hardest thing about this (very lore friendly) idea is the queue system. If I queue up solo, do I get randomly put with Adders (GC) or Maelstrom (FC)? Can I duo-queue with a Flame who is in a different Maelstrom FC? Do you get placed with a random company if your party qualifies for two?

I'd suggest that it works like this:
-Solo queuing places you in your own Grand Company.
-Party queuing is only available if your entire party belongs to a single Grand Company OR Free Company.
-If your party is a group of individuals that belongs to both the same GC and FC, the GC takes priority.

This makes it so there's no distinct advantage to joining an FC that's not under your GC.