I'd go to Bryce Canyon and camp up there rather than spending 1 1/2 hours each way every day you want to go up there. Three hours drive time is more than it takes you to break and set up camp. It's quite a bit higher elevation in Bryce so much cooler in the campground. Again, there's a great shuttle system there, too. Drop into the canyon at one place and come out another, using the bus to get back to your car. Bryce Canyon is another place to hike in the mid to late afternoon as the main part of the "canyon" faces east and gets shaded in the P.M.
Escalante is a huge area. If I had to pick the main things to see it would be Lower Calf Creek Falls and Spooky and Peek-a-boo slot canyons. For camping, you might look into camping at Singletree CG north of Boulder up in the NF. At over 8000' it's far cooler.
Timing: At a minimum I'd plan two full days (three nights) at the south rim. At least two full days at Zion (great hiking). A full day (two nights) at Bryce so you can do an extended below the rim hike.
For your route to or from the South Rim from TX, consider taking NM 63 and visiting El Morro NM. We've been to a lot of NP's and NM's and this one was quite surprisingly interesting. Plan on three hours or so for a quick tour.
Also, whether you do a day trip from the south rim or you camp at Bonito Campground near Sunset Crater north of Flagstaff, there are several NM's to visit near there. Walnut Canyon and Wupatki NM's are worth a day between them.