I am comming up over hills pulling my camper at around 50 mph and the 350 is tacking pretty high.
Are you looking at a tach, or just listening to the engine? If the 350 is under 4,000 RPM, you're not likely to be doing any damage. The 4L80 is a very good transmission. It's rugged, and the gear ratio spread is about right for most engines. I run a 454/4L80 setup in a 35 foot class A motorhome, and I have no problems pulling most hills. It does wind up a little on a long uphill pull in direct drive, which sounds like the same situation you've got. The big block definitely has a lot more torque than a 350.
Jerry