Another thing you could do is to not take I-70.
Before you even get to Denver, drop down on one of the state roads (perhaps 287 at I-70 and Seibert or Hwy 71 a little further west at Limon, CO to south of Pueblo, CO. At Walsenburg pick up Hwy 160 west. You will have one major pass to go up and down - Wolf Creek Pass between South Fork, CO and Pagosa Springs but it's nothing like climbing out of Denver on I-70. Plus, Wolf Creek Pass is less 'Pass' miles. It's multiple lanes and a very good highway. Like all mountain driving, take it slow and get into low gear before you even start descending. There are always pull-outs to cool off and enjoy the scenery.
After the Pass plan to stop for a night or two in Pagosa Springs and do a soak to relieve that tension. :) There are immaculate concrete pools of varying temperatures and it's a relaxing way to spend a couple hours moving from pool to pool. It overlooks the river and the little town - quite pleasant. Pack a little cooler for drinks or food. There are plenty of patio tables.
Continue west to Durango - another good stop. Take the train or your towed vehicle up to Silverton for a nice day trip.
Continuing west to Mesa Verde Nat'l Park and do a ranger-led walk to the ruins.
At Cortez pick up Hwy 491 which will take you to 191 north to Moab.
This whole drive is a beauty. We rarely take interstates. There's more to see off them; you don't have to get through big cities and you'll have a lot less traffic.