I just stayed at Smokemont a couple weeks ago in my truck camper. I had no reservations. You should be able to get a spot during the week. Probably not during weekends. There is a separate loop in Smokemont for larger RV's. Depending on when you want to go...you may consider going in cooler weather and using an ice chest.
I've stayed at Cove Creek, and Cove Mountain RV Parks in the Townsend area. Also "Camping in the Smokies" at Gatlinburg. All in our 5th. I didn't like any of them.
I would say of the CG's I've seen inside the park, Smokemont may be the best bet for a larger RV. Cades Cove and Elkmont have just a few larger spots.