You shouldn't have to remove the aluminum shifter plate. When you get the trans out, take a large drift and hit the 3 plate bolts to shock them, they should come out, except for the ones you have stripped, have to weld a nut onto them.
As far as removing the trans, I always have used a floor jack. Remove the cross member and let the trans down some, you need to support the engine somehow, another floor jack or engine hoist. Then, just wiggle it out. When you reinstall it, cut the heads off 2 7/16x 2 " or so bolts. Screw them into the top 2 trans bolt holes as guides for the trans. The trans probably won't go in like hot butter, the guides will assure alignment and give you time for a break when your arms are ready to fall off. This way, the input shaft isn't trying to twist the center of the clutch disc while you are resting. Your trans jack will work too.