OP, do a search on "Darby Wells Road"; lots of boondocking space in the BLM area there and all around. Pay attention to what appears to be "hard surface" but isn't!
The campground in Organ Pipe NM is lovely; large, paved, well-spaced sites, beautiful surroundings, a dump station, water, and nice showers. If one has a "senior" or "access" pass, camping is pretty cheap.
Any "dangers" in this area are overblown; yes, one has to use common sense about where one camps and hikes, but that's the situation pretty much *anywhere*. Stay aware of your surroundings and enjoy the beautiful area!