Can you take the Yukon back and get one with the NHT package or better yet the Ford Expedition with Ecoboost?
RV tow ratings for half tons are typically limited to tongue weight or payload. But your limit will be performance/perception bcause of that 3.08 gear. Even thought the 6-spd trans really helps, you'll be cruising on flat land in 4th gear at 2500rpm and down to 2nd gear for those mountains at 5000rpm. Truck will be fine, but will the family?
The typical RVer adds over 1000 pounds of camping stuff over dry ratings based on a survey done in the past. So 5k dry will be 6k loaded, more with full water. So you'll be right at the 6300 pounds of tow rating and whatever your GCWR is.