Welcome to the CAC
Unfortunately the original poster doesn't seem to be a member here anymore. I have no idea if this project was ever completed.
Narrowing the rear frame seems pretty straight forward with the body off. Figure how far you need to move the side rail in to clear the tire you want to use then cut the total amount out of the center of the 3 cross members in the kick up rails. Then move the side rail in to the required width and weld it all back together after a ton of measuring to be sure it's all back where it needs to be. Some extra plating and gussets would be in order too.
The differential cross member will need narrowed and adjustable length strut rods from the aftermarket will have to be used. The stock spring won't work and the trailing arms and shocks don't allow much room either. A coil over kit with offset trailing arms like this one from
CorvetteMods.com
would be a good way to go to give some extra clearance and solve the spring/shock issue. The half shafts will also need to be narrowed and brake lines modified. Custom offset wheels may be necessary to center the tire between the outer body and the frame rails.
Also you will probably need a fuel cell sized to the area you have left to mount it. And of course the wheel wells and floor mods so the body will set down on the frame again. There might be a good argument for side pipes here as well as the spare tire carrier won't go back in.
I probably missed something.
LPE used to make a larger half shaft for drag racing but I don't see them on their site anymore. Also
here's a good article on upgrading the C3 driveline for higher horsepower.