Towing in 3rd gear rpm high?

Hey guys new to the towing a travel trailer and I Have a 1996 Silverado extended cab 4X4 with 5.7 Vortec and factory 3.73 gears and factory size tires 265/75/16 and the truck only has 50K original miles. I'm towing a 21ft Wilderness bunkhouse camper dry weight I believe is 3850lbs (at least that's what the salesman told me) My truck loaded with firewood and all the rest of the goodies im guessing I'm towing around 4500 to 4700lbs. My truck can not tow this camper in overdrive without upshifting and downshifting so I was told to just run it in third gear which in this truck the owners manual says to do anyways to keep transmission from overheating. The problem is at 60mph in third gear I'm at 2400 to 2500rpm! The truck pulls it no problem in third gear but the rpm being so high for a long distance is bothering me. I was thinking instead of doing 4.11 gears because I still don't think I could keep it from downshifting of doing 3.42 gears and when I replace my tires to go just one size up and that would put me at 2300 to 2350rpm at 65 in third gear. What do you guys think?