The question is, do you actually want to visit Phoenix, or just use it to fly in and out of ? I ask as you have Vegas on your itinerary. If you have no real desire to visit Phoenix, then you could save a couple of hundred miles, which in turn saves gas costs and time, making it slightly more beneficial using Vegas [Other than additional flight cost [$?].] I would also try and squeeze in Monument Valley and Capitol Reef NP that would include a drive along Utah scenic Byway 12 between Bryce canyon and Torrey.

It would look something like this; LV>Zion>Bryce>Torrey [Capitol Reef]>Moab [Arches/Canyonlands]>Monument Valley>Canyon De Chelley> GC South rim [Cameron Trading post on route or overnight]>Sedona>LV [Possibly via Seligman on route 66 and Hoover Dam.] I would leave GC till near the end of the trip as a highlight and to enter the canyon east to west as mentioned by Buck. The loop would work from Phoenix as well, just adding those miles at the start and end of trip.