Personally I would do a day trip to Goblin Valley (2 hours from Moab) instead of time spent on the white rim trail.
If you went to Goblin Valley you could then drive down Wild Horse road (turns off just prior to the state park) approx. 8 miles to some purple mounds (similar to yellow mounds in Badlands N.P. but purple), great colors with the San Rafael Reef in the background. And, the San Rafael Reef is photogenic in itself.
If hitting Monument Valley on the return trip you could take 89 (or 89A) on your drive to Moab, West through Kanab, head North to hwy 12, hwy 12 to Torrey then hwy 24 to Hanksville and hit Goblin Valley first, this route adds 3.5 hours over the more direct route to Moab.
Of course this drive could add a whole lot of other stuff like Bryce Canyon and Capitol Reef N.P.
On your drive to Monument Valley to could go West from Blanding and see Natural Bridges National Monument, then South on 261 to Goosenecks State Park.
There is just far to much to see in Southeast Utah. Anyways just throwing other ideas out there.
Tony