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You state you have a 350 transmission, which is an automatic. The car does not have a flywheel, it has a flexplate. The torque converter is bolted to the flexplate and the transmission input shaft connects to the torque converter. I believe you need to pull the trani.
No matter which way you do it just be sure the distributor and/or cap does not rest on the firewall and the fan blade does not break the fan shroud, in other words you need to solidly support the motor so it does not tilt back to far. I use a bottle jack and a plank of wood under the oil pan. Good luck,,,,Peace,,,Moosie
If I remember correctly, cant you install longer trans to engine bolts and slide the trans back enough to remove the flexplate? Of course you would need to remove driveshaft, trans mount, and converter to flexplate bolts, etc before sliding back (make sure converter slided back with trans). And as moosie982 said you dont the assembly to tilt. Using a long box end wrench reach into the space between the converter and flexplate and disconnect bolts holding flexplate to crank. I've done this on a few cars and I believe it will work on the vette...but not 100% sure. Can anyone confirm?
If you have all the bolts out and the converter unbolted, Try to put a floor jack under the trans pan with a wide piece of wood and move it back some. I really do not think that you will get enough room before the pan hits the mount. Just bite the bullet and drop the crossmember and take the trans out. Good time to change the front and rear seals. Would only take an extar 45 minutes with air tools
I just got done doing this job tonight myself. All I had to do was unbolt the trans and slide her back a few inches to get to the bolts. It took about 5 hours but I was also replaced the starter and was checking the engagment. I took my time and did this job by myself without any help. I drove the car up onto the ramps and then jacked the back up on to jackstands so I would have ample room to play under there. Disconnected the shift linkage, trans cooler lines just be on the safe side. Used a floor jack with some wood and just slid the trans back far enough so I could get a wrench in there. You do have limited space in there, the trans dipstick was a fraction of an inch away from the firewall. I'm happy now that this is done and it wasn't as bad as I thought it would be.