You need to rethink your plans for three reasons.
1. HOT! You're wanting to travel in desert areas, in the summer. You'll need a/c the entire time, meaning electric hookups. The only campgrounds in those national parks, that have electric hookups, are GC and Zion.
2. Since you're looking to stay in popular spots in the summertime, you'll need to make reservations the second they're available. There will be extreme competition for them. Expect to lose out on some.
3. Your plans are very ambitious since many have no idea how big the West is and how long it takes driving from place to place.