Are you starting the CT from Denver or Durango?
If your going to Durango, then the North Rim of the Grand Canyon isn't too far out of the way. The Kiabab Monster Cross
http://www.bikepacking.net/routes/kaibab-monstercross/ The Rainbow Rim riding right next to the canyon, even if you drive out there, it's awesome. You can add gravel out to view points in the park, and finishing the AZT, night riding advised for the climb back up, can also be added. It will be monsoon season so expect an hour or so of heavy rain mid day, there's lightning as well but it's not Colorado, your never that exposed.
Tim