You can't do Bryce Canyon as a daytrip from Vegas, it is just too far away. Its also a challenge to do both Zion and Bryce Canyon in a day even if you didn't also have to add in 8+ hours of driving, to do it as a round trip from Vegas. If you have your heart set in staying in Vegas, Zion is close enough to just do that as a daytrip, but skip Bryce. Otherwise, a perhaps better idea would be to try to stay right near Bryce, and then instead of backtracking to Vegas, start making your way back to I-40, either going past the Grand Canyon, or even spending more time and working your way to Albuquerque via Monument Valley, Mesa Verde, and/or Santa Fe.
For your New Mexico section, unless you really have your heart set on seeing El Paso, I'd head to White Sands and then go to Roswell, again to avoid backtracking. You could spend the night right in Roswell, which would give you time to stop at Carlsbad Caverns on your way to Fort Stockton the following day.
Based on what appears to be your strong interest in cities, I'd look at adding Austin to your itinerary. If you want to see any of LA, then I'd look at more time there, as right now, you really have no time available to see much anything, once you factor in how big LA is and that you'll need time to pick up your car.