How can I repair drywall which has bowed away from the framing?
Trimming the bottom will not create moisture issues--nearly every wall in existence has a gap at the bottom. If you're relying on drywall to handle moisture you should hang up your hammer.
Trim away, and if the drywall offends thee by refusing to lie flat, pluck it out.  Drywall is cheap and if it's behind tile anyway you can patch in as you see fit. Either cut on studs and patch it in, or cut between studs, float new backing, and screw it all together. Drywall behind tile doesn't necessarily need to be taped. If anything, use fiberglass mesh in your tile mortar.
Also, bathrooms are not boats. They needn't float. I've build and owned hundreds of bathrooms and I've never caulked baseboard. I'd rather have some airflow after a splash situation than a sealed floor that takes forever to dry. You will not keep it from leaking if you flood the room.