We've driven our 40' MH on dirt/gravel roads because we love boondocking. We did have a side radiator though. However, I understand that this road is very rough at times but they do grade it. If you are considering going I'd call the park right before your drive to see how the road condition is or drive your towed vehicle down it first.
Here are the campsite photos:
Some looked very doable for a 40' rig. However, again, I'd call the park to see their take on it and perhaps they could help with a site number of one of the big sites so you could reserve it.
There really aren't any RV parks nearby except in Bloomfield, NM. Good luck!