2013 Tahoe for towing.

[draino76]

I own a 2013 Tahoe 5.3 6spd with a Black bear tune. I recently bought a 24" travel trailer that weighs in at 5,500 pounds dry with a 900 pound tongue weight. I have an r4 sway/ weight distribution hitch and it seemed to pull well. After about 400 miles I hit some pretty stout hills before the Rocky mountains. Another 100 miles and the rear end began whining. I pulled over and could hear the rear differential fluid boiling. I cooled it down and limped it into a dealership. The gears and oil are shot. The unit has 308s. Is it worth it to install 373s and all the equipment required to keep all the other fluids cool or take the money and upgrade to a newer Duramax? We plan on at least one long distance trip a year 500+ miles and many of them through large hills or mountains. Most of our daily driving has been passed on to the Chevy Volt we recently purchased. All advice is appreciated.