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Try to get the car as stable as possible. I would suggest tall ramps, which would allow all 4 wheels to remain on the car, but allow you to get under the car.
The Corvette has a pretty small transmission tunnel, so I doubt there's enough room to simply unbolt the tranny and slide it rearward enough to remove the flexplate.
You'll need to unbolt the drive shaft, as well as the crossmember. I suggest getting your hands on a tranny jack, as a TH350 weighs about 150 pounds, and can be a bear to wrestle around. Then remove the flexplate bolts, slide the torque converter back a little, unbolt the shifter cable, remove any vacuum lines that might be from the tranny to the engine, then unbolt the tranny from the engine, and "drop" the tranny.
Does this have anything to do with your other post, about the vibration and starter that's hanging up??
Yes it does. I am redoing the hole car myself. All new wires everything but i wanted to make sure that i didn't have to buy a new engine. So i tried starting the car with the old screwdriver and the starter wasn't engaging the flywheel. I then shimmed it out and watched the flywheel. It looked like it was wobbling? When it ran for a hole 10 min 6 months ago in park it sounded great. When driving there was noise coming from that location.
The mechanic if that's what you want to call him said that the starter would keep engaging and disengaging. I recently had someone else rebuild the trans and but in a new and better torque converter and it ran fine.