Either way, when I put it in reverse, it pops out of gear unless I am keeping pressure on the gear shifter.

I would specify which transmission I have, but I havent got under the car to confirm which one it is.

but its either a t56, or a ZF...

Old owner, said a long time ago engine/trans/rear end all came out of 96 LT4 Vette.

I havent been under there to verify if the rear end or transmission is a fabrication job...