Sounds like a great plan to me! I have camped at several of the "roadside" sites including Grapevine Hills GH#2. That one, like most of the non truck/4wd accessible sites have mainly low desert vegetation. I have always had a coyote chorus especially early before daylight at the low country sites!
If backpacking is possible I would definitly do a high country trip as Al mentioned!
Here is a link to the roadside camps info if you have not already checked it out.
Big Bend National Park - Backcountry Roadside Campsites (U.S. National Park Service)
Will be looking forward to a trip report and photos!
Maury