You may have seen this already, but: https://www.nps.gov/bibe/planyourvisit/bc_outermountainloop.htm ... My favorite part:
If you go through with it, you will probably want to truly appear like you know what you are doing when you check in with the rangers/whomever, so they don't try to stop you from going.
But, yeah, there are a couple of spots to cache water (food not allowed in cahces, but looks like you're good for that). I wouldn't worry about people stealing other people's water. There is like NO ONE out there. I would plan to not depend on the natural water sources at all.
Hopefully you will have some clear days, and you can clearly see the rolling hills out into Mexico for many miles!
Now, the Guadalupe Mtns. are slightly less desolate. I don't recall the logistics of that trip as much, except parts of the hike were beautiful!
One last thing before I forget: When you hit up Guadalupe Mtns, you should DEFINITELY take a half a day to cross the border into New Mexico and check out Carlsbad Caverns. It is really funny how it just looks like there is nothing there -- just a couple small buildings off the highway in the middle of the desert -- then come to find out that there is an entrance to a massive cave there! It's amazing.