If you are going to be in a hurry, the why not take I-20 to I-10. Yes it will be warmer, but your dash A/C and the house ACs should keep you plenty comfortable. I had to go from San Diego to Houston in August on two occasions. Not a big deal since we drove all day anyway.
For the return, take 40 and stop at the Grand Canyon, Santa Fe and Palo Duro canyon in Amarillo.
I am happy to suggest rest area overnights and RV parks along either route if you would like.