I'm not sure if the Caprice is the same as the Roadmaster, but you are approaching the top of the recommended RMW envelope of 7,000lbs, even with a weight-distributing hitch and 750lb bars (don't forget sway control and disconnect the air compressor for the shocks). That said, I have towed that kind of weight with my old 92RMW without any problems.
I wouldn't worry so much about the rear end as the transmission. In my experience, that's the weak link. I'd certainly change the fluids and an additional tranny cooler wouldn't hurt, but if you are doing serious distances, I'd consider having some HD components installed (like the sunshell). Electric brakes are a must, but make sure the car's brakes are in tip-top shape as well. Same goes for front end linkages, etc.