Your truck is 24 years old. That 1992 350 with 5 spd and 4.56 gears should have no problem towing 10K. Apparently its tired. I tow that much with a 5.3L (smaller than your 5.7L), 6 spd auto, and 3.42 gears. I also towed a camper that weighed that much years ago with a 79 Chevy 4x4, 350, 4 spd. manual and 3.73 gears.
If your truck body is in good shape I'd suggest buying a rebuilt truck 350 engine at your local auto parts store and drop it in with a new dual exhaust system. A lot cheaper than buying another truck.
george, I like this idea. Maybe even replace it with a 454. Before I get too far into this, I need to do a little more homework. Hate to put all that money in if I am way over weight to begin with. I will check some prices and see how much monkey business this could be. Thanks.