During our 16 years of full-timing and traveling constantly - mainly in the western mountains, we saw many, many gas motorhomes in the same places as our diesel went. Yes, you can drive in the mountains with gas.
You mentioned full-timing so you'll need to study the carrying capacity carefully. Remember, when you full-time you carry everything with you. It's not like going on a vacation. This also includes the car you tow.
You mentioned looking at a 36-40' and before someone chimes in that you can't stay in the national parks with that size, I just wanted to let you know that yes you can. We did it successfully.
Good luck in your search.