We took this route in the opposite direction in 2010. A few slight grades coming out of Provo (beautiful senery). Once you get on the US16 there are some 5-6% grades you will face as you climb the mountain. Should not be a problem with your rig. Evanston has diesel fuel as does a few stations on US16. Are you staying at Colter Bay RV? We did the float raft and took a tour van of the area. Lots to see there and not nearly as crowded as Yellowstone.
Please make sure to take plenty of pictures and post them for us!:)
Have fun
