The RV length on the Chisos drive is a "recommended" 24'. Since you're so close to that length why not ask a ranger if you can drive it?
Also, there are plenty of wonderful hikes to be done without going up to the Chisos:
Hikes in Big BendI really think you'd like Rio Grande Village campground the best...the dry camping area. Part of the campground you can use your generator and you definitely won't need your air conditioning in December!
Cottonwood campground is nice but it doesn't allow generators and there's no dump station.
Explore the above Big Bend website for lots of good information.