Rbaart,
Yes, renting an RV is expensive, but so are H/motels and restaurants.
Our own coach is only 23ft and we find it adequate, but not spacious and we have lived in for more than a month at a time often. The fuel consumption will vary little until you go over 25ft.
In May, campgrounds will already be crowded on weekends. There are a number of smartphone apps that can assist you to locate places to over night park (ONP). You will need a US enabled phone.
The majority of roads you should encounter will be suitable. I will advise that you not go anyplace that you do not see passenger cars. American trucks are very large on an international scale and most roads are adequate for them.
Now, you are thinking of a 4000 mile excursion in 35 days?
Many RVers limit a day to 200 miles. Very experienced and hardened will do some 400 mile days and that is all interstate (like autoroute). This still is very tiring. What you don't seem to have allowed is that the best speed for you will about a 60MPH average. Then, this has to include fuel stops and meal breaks. So, your outline has the potential to be 20 driving days and not much sightseeing. I have not worked your route, but I am not sure it is even actually possible to enjoy the planned excursion.
You will be able to get a lot of advice and support here if you stay in touch along the way. With a tablet linked to a phone, this will on be difficult along the interstate routes because cellphone coverage there is adequate.
I hope this is more of an help than a discouragement. There is a lot to see in the USA and the two of us been working on it for years.
Matt
Matt & Mary Colie
A sailor, his bride and their black dogs (one dear dog is waiting for us at the bridge) going to see some dry places that have Geocaches in a coach made the year we married.