How heavy is your TT and do you have the towing package on the truck. Either the southern or northern route is going to run over some high passes. Wolf Creek Pass in the south or I think Eisenhower tunnel in the north. I believe Eisenhower tunnel has a notoriously long grade and is used by truck reviewers to test trucks. But being on an interstate the grades are limited to 7%.
We never had a problem with either even when we had a F-150 5.4L or a Suburban before that. Most of these passes are around 11,000 ft as are a lot of other Colorado passes.
List of Mountain Passes in ColoradoFace this fact, you will be climbing mountains once you enter Colorado past the front range.
Oh yes something just occurred to me, the pass in RMNP is 14,000 ft to go from the east to the west side and I don't think they allow you to tow trailers over it. You should check before you make plans.