All those places you mentioned, with the exception of North Rim of the Grand Canyon, Colorado, and Bryce, will be well over 100 degrees.
North Rim, Lake Powell, Utah, and Colorado are the only places you will need a reservation. Most people don't go the other places you are going that time of year because it's about 30-50 degrees too hot.
Hope you have dual ac's, and find some shade. I would not recommend primitive camping, with no hook ups at any of those places, especially if you are bringing animals with you.
Have a great trip!
