First, I'm not going to say where you should and shouldn't go since there isn't time enough to enjoy half of what you have outlined, and that's coming from someone who was born, raised, and lived his entire life in the area.
Secondly, it is simply the most brutal time to visit the Southwest with only the Grand Canyon offering a brief respite from the heat, although it will be hot during the day until a possible monsoon storm passes briefly through the area in the afternoon.
There is no doubt the trip you have planned is an awesome trip with more time and a few more sites added, but I'm sure you would not suggest some one see the wonders of the New England region in the dead of winter either. Here's hoping it's worth the expense and effort.