Elevation isn't much of a concern. You won't get that high! You don't say what you are using for a tow vehicle but I presume it is a diesel pickup. If that is the case you will not see any drop off in performance at the elevations in that vicinity. However, some of the grades can be pretty steep and the curves pretty tight. Not so steep or tight to be of concern.
I went to high school in Sundance, WY and have traveled all the roads extensively. I still have family nearby and visit often.
Click on this MAP
. The blue route is the one I would take.
I have stayed at both the KOA at the entrance to Devil's Tower and the campground inside park. I found both very nice.