Not tearing the carpet is an incredible feat!
I've definitely pulled the manual trans out of my 93 without cutting/removing the Y-pipe, but I did have the torsion bar crossmember and front diff out. Was a bit of a puzzle to get the transfer case tail housing down past the fixed crossmember, but it is doable. Front diff is very annoying to get back in because of the weird balance, but torsion bars and crossmember are pretty easy, even if a few rusted bolts give out (as they did for me). For posterity's sake, pulling the Y-pipe down off the manifolds early is very nice. With that and the trans mount disconnected, the motor mounts allow quite a bit of forward/backward tilt which can make reaching those top bell housing bolts easier.
For install, I found it handy to cut the heads off a couple of spare bell housing bolts and thread them into the block. Definitely not necessary but helped a bit with aligning trans and engine. Also, since the engine can move so much it can be hard to eyeball the alignment. Having someone to watch from a wheel well while you wiggle and push is very nice. Not sure if any of this is helpful at all, but good luck!