Certainly not the TH350 that is in the Corvette now. To keep the diesel motor happy at freeway speeds it will need something with an overdrive. The GMC pickup has a 4L80E which is a very robust transmission. It's also quite a bit larger and longer than what's in the Vette right now. It would probably be possible to stuff the 4L80E into the tunnel but that looks like a really tight fit and a lot of trouble. Plus, I would probably lose about an inch of precious ground clearance.
The 700R4 would be a good choice. It has a nice low first gear for good off the line response and a nice tall overdrive for relaxed freeway cruising and good fuel economy. Then there's the 4L60E which is a computer controlled version of the 700R4. I would have to use a stand alone aftermarket controller which complicates the installation a little bit and adds to the expense. One nice advantage to the 4L60E with aftermarket controller is all the shift parameters can be dialed in without digging in to the valve body. The controller will also support the use of paddle shifters. I would like that a lot.
For the time being I can get a lot done without having the actual transmission I'm going to use. I'll leave the TH350 in there for now and bolt the 6.5 to it (no torque converter or flex plate). That will give me an accurate motor position and I can work on plumbing for the turbo, modifications to the thermostat housing, wiring, fuel supply, etc.