First off I am motorhome over travel trailer for such a trip, where it sounds like you will be spending a lot of time on the road.
The second point that I want to mention is that I have seen message threads posted by foreign visitors to the US doing much what you describe where they managed to work out deals with used motorhome dealers to buy back a motorhome at a pre-set price after 4-6 months, assuming it was still in good condition. This allowed them to avoid a rushed private re-sell in the limited time they had before leaving the country and was still cheaper than renting.
Also if you end up with a small class C it is certainly possible to travel without a TOAD. We have a 28 ft class A, and no TOAD, we have put over 7,000 miles on it since buying it in 2016 and have been able to get into see 90% of the places we would want to go without a TOAD. Though this does require a bit of planning, sometimes using taxis, shuttle buses, etc. Though at under 30 ft and with a 178 inch wheel base we can easily fit into 2 standard parking spaces end to end, or back in if in a location where we can over hang a curb.
