Well, since you are trying to get to Moab, I assume you picked Keystone as a possible layover, due to distance traveled. But, most of the land close to I-70 is private. I can't think of any boondocking possibilities for a rig your size, close to I-70, especially that early in the summer.
As you head west from Keystone, you will still find mostly private land (no National Forest) along I-70. You would have to go at least 30 miles off if I-70 to get to any National Forest land with camping prospects. Again, though, that time of year, you will likely have lots of mud, and many gates will still be closed.
I would bite the bullet and look at the two NF campgrounds by Frisco (other side of Lake Dillon). Or, you could head north on Hwy 9, and go to Green Mountain Reservoir. N39.867569 W106.278065. Lots of NF campgrounds around that lake. Not many trees, but you may want the sun on your unit to warm it up without so much propane.
Look at GoogleEarth, and turn on the National Forests. You will see the boundaries, and see how far you may have to travel from I-70 to get to the forest.
Good luck!
2017.5 Lance 1995
2017 F150 EcoBoost, Max Tow
Most camping off-road