all of the above replies will be relevant.
As I titled the answer, ALL of the above replies are relevant. You need to look at which transmission to look at for fitting in you baby.
The 6 speed ZF and Richmonds will require much alteration to the trans tunnel, and IF I remember correctly, you'll need to put in a new bell housing and while you're at it a new clutch isn't a bad idea.
The cross member and mount will in all likelihood need to be rebuilt due to the length of the tail piece and where it mounts, then you'll have to cobble up a new drive shaft if they were shorter, or have it shortened and re balanced if it is longer.
The Warner T-5 series that was used in the F-bodied cars may not stand up to the torque that the corvette makes, but may be an easier fit, but I also remember something about them being installed about 20 to 30 degrees out of the verticle, and needing a "special" bell housing to remedy this and if I remember correctly Advance Adapters used to make them, (I'm reaching back atleast 10 years now.)
It just struck me as I was sitting here, ZF used to make the 5 speed transmission for the 1/2 and 3/4 ton trucks, from 88 on forward. They should be strong enough, but doubt they would go in easily, but you can take a look at it. I would consider shortening the shifter though.
In the long run, you may be better off rebuilding the 4+3.
An other idea is looking for an 80 to 87 T-10 which was built as an overdrive 4 speed for Mopar and GM truck products. External dimensions are fairly close, you only have 4 forward speeds, but the top one is 22 percent overdrive, great for the highway!
Keep us all informed how your hunt goes, and I'm rather certain we'll all input our own two cents.
Taegdh