You are not crazy but you will need to be informed about camping options where and when you plan to travel. You will not have any difficulty driving a 35' coach on any of the roads you will need to travel. So time of year and camping locations just need to be confirmed before you go. I really like RVParky.com and it's available on the web as well as an app on your phone. Google Maps will get you where you need to go and keep you on the main roads until you get close to your location. I started my RVing life the same way. Rented 3 different RV's as needed which really helped when I decided to buy one. I never had a problem with any including some time simply dry camping and using the generator for power.
As I recall there is NO camping near 4 corners but 4 corners is not too far from several tourist areas including Cortez and the Cliff Dwellings, a must see. The visit to 4 corners takes maybe an hour so you will have plenty of time to fit this in along your travels. It is not a destination.