problem with backing.........help????

[69 air cab]

I just finished changing out my 305 with a new 350 engine on my 84 Silveradlo. I had the original 350 tranny rebuilt due to the major leaks and it just barely moved. I put a tranny cooler pkg on it, new hitch, new brk. converter.........all to tow my camper. MY PROBLEM.........on a steep (or not so steep) it won't back (push) my camper up a hill. You can floor it and it won't move.
Do I have a tranny problem, rear end problem or brk. problem? Any suggestions on what to check first and how to correct? I did do a brk job and even wonder if I may have screwed up the backing adjustment. Anyway........I really need some help.......thanks in advance for any advice. OH......I did put a new 600 cfm carb on it to thinking the old quad. was the problem.