The "sliding the crossmember back" idea works for A-bodies like GTO's they have two sets of holes in the frame rails for the same crossmember to be used on TH400's and ST300's. Firebirds have only one place to mount the crossmember. What you need is a crossmember that's intended for a TH400. This crossmember will mount to the car in the same place, but the transmission mount will be further back. Maybe that's the U-shape you describe.

I reached all of the transmission bolts from under the car. For the ones that were a long reach, I used long extensions and a u-joint on my socket. Don't unbolt the engine from its mounts. You're not going to slide it anywhere. I don't have headers. I don't know if they're in your way. The A/C equipment is not in the way when you work from underneath.