RVs get snapped up pretty quickly in the SFO/RNO area...there may be some still available in Las Vegas/LA/Seattle/Portland, but picking up one there would require a change in airline plans.
That said, a week on the playa is survivable without an RV. Granted, an RV solves a lot of logistics issues, but more than half the denizens of Black Rock City make do with tents and associated camping equipment...even a semblance of cleanliness can be maintained with spray bottle showers and baby wipes.
I take an RV, but we use it only for the meal prep. Besides NEVER using the RV toilets (we use the BRC porta potties), we all sleep in tents outside for gear storage and privacy...7-8 people sleeping/peeing/pooping inside is pure chaos.
Good luck on your search!
Don't bore your friends with all your troubles. Tell your enemies instead, for they will delight in hearing about them.