For the late-game battles, I ended up parking my entire crew (~5 red shirts, 2 yellow, 2 blue) in one of the weapon rooms and just allowing the rest of the ship to catch fire and breach around me. I'm not sure if there's any other way to handle the flood of enemies that the game throws at you.

The one weapon room was just a death trap and since the shields automatically go back up after battle (and it doesn't seem like your ship can be destroyed), you can repair it all after the fact without worrying about your crew being sucked into space.

It wasn't a particularly fun strategy (and not something I feel should be allowed or encouraged, mechanically), but it's what got me through the end of the game.