To be honest I wouldn't go anywhere near Phoenix. The rest will depend on how much time you want to actually spend in SD. So Saturday get an early start to the canyon so you have a good portion of time to enjoy the views that day and stay in the NP or nearby. Sunday revisit the rim for a couple of hours and make your way to 29 Palms. You could take the old section of route 66 through Oatman. Then Monday drive through Joshua Tree NP early and spend the rest of the day and part of Tuesday in SD. If you want to go direct to SD you could go through the Prescott National Forest and join I-10 near Brenda and then take CA78 south to I-8. That's about 70 miles shorter than going via Gila Bend.

You will need to watch out for one way drop off fees on a one way rental. If that's an issue and SD is not a must you could simply visit the Grand canyon, Monument valley and Sedona and head back to LV. Personally that's what I would do.