Your giving me a bad case if hitch fever talking about your trip.
Tire size and gearing is critical. My 06 K3500 would look so much better with 285s but I would need to re gear to keep Duramax and Alison in the sweet spot. When I left California December of 14 I pulled a 36ft fith wheel to Carson City Nevada then on to Hurricane Utah, thru North end of Grand Canyon to Santa Fe NM. From there were came across to Knoxville TN. We had been living in the fifth wheel for 15 years and accumulated to much junk. I scaled it before leaving CA and was only 500 lbs below max for the truck.
Kept an eye on EGTs and let the truck do its thing. Sure was glad I had this truck and not my 94 K2500 it would have been to much for it even with the five speed. Managed to enhance millage on my trip by finding a semi to pace with and just slide in behind them. I could tell when I hit the sweet spot, boost would drop along with EGTs.
Yo have a sweet ride there I hope you enjoy it for a long time.