Or just have a lot of the Starfleet crew be killed by being pulled to the DQ and have them be replaced by various DQ aliens being held on the Caretaker's Array. That would give them a more immediate connection to the DQ and better ways of fleshing it out.
Oooooh, I like that idea. Just the concept of the federation portion of the crew being outnumbered and forced to live by and answer to a different set of rules and ideals on their way back home. Very interesting!
And unlike the Maquis, having the crew be DQ aliens would give more connection to the DQ and more ability to flesh it out and give them external plots to drive the show.
Plus, with around half the crew not being from the Federation would raise the question of what would happen to them if a way back home WAS found. Because the Federation isn't home to any of them.