2002 Monte SS no reverse when warm

[MonteandVortec]

I bought this Monte Carlo SS from a dealer, used. It had 82000 miles on it. Everything seemed fine when I test drove it except it needed new brakes and a new wheel bearing, which didn't bother me as I actually kind of like doing brake and suspension work. Anyway, blunder of all blunders, I never put the car in reverse when I test drove it, and as it turns out, it has no reverse when warm. It will reverse fine when cold, but after even just a 2 mile warmup, it will not reverse. The tranny works perfectly every other way. Being that I bought the car 'as is', the dealer is free and clear. I managed to get a hold of the previous owner, and he told me he had the tranny rebuilt last summer, and the shop that rebuilt it told him if he ever had any problems, to bring it back and he'd fix it. He was really surprised that the tranny is acting up because he thought it was perfect. There's only about 3000 miles on the rebuilt tranny. His wife wanted a Pontiac Vibe real bad, so they traded the Monte to get it. He said he traded it because it went through too many wheel bearings and rear brakes, and he was sick of having to pay to have them replaced.

As lucky as anything, that tranny shop closed shortly after the rebuild (he was a good and reputable tranny man in the area, not a fly by nighter), and the proprietor is now driving truck in the NWT 2500 miles from here. The previous owner of the car told me he'd have the tranny shop owner fix the tranny for 'him' (me) if he could get a hold of him. That is not happening.

The car is practically useless like this, because it's pretty hard to go anywhere without having to back up at some point...

Could it be a piece of dirt (from a dirty rebuild environment) in a valve? Would a flush help? Or is there some sensor that might need replacing? It's like $3000 to rebuild the tranny in a shop, and GM wants over $5000, which puts the total expense of the car far, far beyond it's actual value, but it's no good like this, either.

Thanks for any advice.