I almost think that you would be better off going the other way around. Go directly LA to Las Vegas. That is a 1/2 day drive minimum.

Do the Vegas thing (are you spending more than one night?).

Whatever day you want to leave, wake up early (especially if it's a Sunday, everybody leaves Las Vegas on Sunday) and then travel down US 93 over the Hoover Dam or over the bypass bridge through Kingman and then East on I-40. I'd stop and stay in Flagstaff. You can do Grand Canyon, Sedona, and Flagstaff in a single day (if all you enjoy doing is looking out car windows) but I think 2 is better. From Flagstaff go in the East entrance to the park, North on US 89A. You can make it a circle by going out the West entrance through Valle and Tusayan.

How many days are you devoting to this part of your journey? You have been all over the boards seeking advice for all manners of Western US travel.