It's a difficult one as there is so much to see and do so at the end of the day it comes down to your choice. I get you want to see things "Quickly" but it feels like your rushing despite having quite a bit of time. If you want to spend a week in total between Austin and LA then I would consider flying from Austin into Vegas and then going to Zion through Page to Monument valley then into the South rim of the Grand canyon via Desertview drive and exit via Tusayan to the south on route to Joshua tree and Palm springs. You could visit the North rim if you have a preference to the the south rim, and even consider Bryce canyon. It's there as a suggestion and as much as I love the Million dollar highway and Ouray, I think you would get more out of your time on the road with the option I suggest.