It think it is too late to get reservations in Yellowstone for July. You would have to stay outside the gate.
Do not go to Yellowstone unless your planning to stay for a week. It would be a waste of your drive time. I would pick one area and do it. Utah will give a great bang for your buck. Zion, Bryce Canyon, Escalante, Canylands, Four Corners, Arches and Maob are fairly close together.
If you want to do the Grand Canyon, then just do that. South rim is way better than the North rim for views. Also, there are Grand Canyon Caverns in Seligman, AZ, and there are other places around Williams, AZ. There is a deer farm that is cool to see. Also, I believe there is a petrified forest not too far away.
Don't spend your whole time driving.
Best of luck. If you want to stay inside of the NPs then you might want to make your reservations soon. It will be hot in Moab at that time.
PS, I love everyone of the areas you are going see. They are all great.
-John