I have a friend that found an old 8600 or 9600 Ford with cab and working heater and good FEL sized for that tractor. He is very pleased with it and can carry out two bales at a time front and rear. In the summer he uses it to push out fence rows, trim back limbs (one working out of the bucket) around fields etc. I think he had about $8K in it however. I know the OP does not want something like that but my point there are safer options out there for $6K. I know locally there is an old but strong running David Brown with a good FEL for about $4K but I would offer less if interested. He has replaced it with a newer tractor.
Best of luck in finding the machine for handling the hay in a safe manner.