I think you could buy another car for parts for next to nothing. They sold a zillion of the GT's for around 10 years.
My guess as to why the gears in the tranny are stripped out is heat. The idler gear should be plastic. The only metal gear should be the one on the top shaft. Those gears spin really fast and the metal on metal will kill the dif gear, as you've found.
I had a cool Alum. diff gear on one of my Gt's. It would last maby 3 tanks of fuel before getting crunchy. I switched back to the plastic and the diff would last six race nights.
If you have the tranny and the brakes, just order the replacement parts to rebuild it.
I'd pick up a new idler gear, diff gear, diff rebuild kit with new rings, and new bearings for the tranny. The larger bearings are likely to be ok as they had really good seals.
I would also rebuild the shocks too.