Can't do it but absolutely love the idea.
As someone who has done most of that -- over two trips and still not all of it -- knowing what I know now, I'd head south after Zion (or maybe after Bryce Canyon). Antelope Canyon in Page AZ is spectacular and not to be missed. But it's out of the way if you do the SE UT parks.
1-2 nights in Page, depending on whether the full-day boat from Lake Powell to Rainbow Bridge is available this late in the year. Other day = Antelope Canyon (best around noon), then Horseshoe Bend on the way out of town.
The other 3 Utah parks (Capitol Reef, Arches, Canyonland) are closer to SLC than to Vegas. Plus they might be subject to park and road closures for high altitude weather. And if you do them, it's a metric sh**-ton of driving. Bryce is also at high altitude, though it's closer to Zion and near the north-south road to Page.
If you do all the UT parks, then do Monument Valley -- its entrance is on the road from Arches and Canyonland back into AZ. You'll need 2 hrs for the self-drive on the unpaved "road" plus at least an hour recovery from that road. Highly recommend the nearby Kayenta AZ Burger King because it doubles as a museum for the World War II Navajo Code Talkers (plus that area is extremely limited).
Also, Sedona is worth at least driving thru and stretching the legs around the visitor center and the chapel, and maybe downtown -- though if you need an extra night's stay, Flagstaff is pleasant and far less touristy and expensive.
