Took me a bit of searching to find a map of Gold Butte NM, so here's the link for anyone who wants it:1
http://www.friendsofgoldbutte.org/gbnm-map/
Looking at it on google maps, it seems the entryway requires going through Bundy territory. I think that might be your biggest impediment to boondocking, not the BLM.
Edit: Yeehaw! New Gold Butte Road has google street view! For the beginning part, anyway. Pretty country, and the satellite view shows fascinating, colorful geology. There's an area called Juanita springs that looks really nice, tho somewhat overrun with ORV trails. I love desert springs.
I'd be afraid to go there alone, though.
