Your post caught my eye, and as it sounds we are working in similar areas. I enjoyed the thread very much, thank you for creating!
Thoughts:
Sheet mulching sounded difficult to me in the desert. I would imagine at minimum the areas would need protection from wind to work. It will take a lot of water to keep it from drying out. Maybe sunken beds?
Alfalfa hay is supposed to be the best mulch money can buy in desert areas. I would spend all my extra cash on it.
What cholla are you referring to? Cane (Tree) Cholla? Regardless just cut it back and take those cuttings to the same place the prickly pears are planned.
I also am curious what kind of juniper? I would be careful to get rid of shade producing trees on your small property, even if they are junipers. Something will grow with them and you could find them useful for wind block etc. I wouldn't worry about them stealing water unless the other trees are up close.
You mentioned a foot down in your soil is hard rock? Hopefully not bedrock? Our soils can be very shallow, especially on slopes 2 degree or greater. It's called listic contact with bedrock or something similar. Where I am you hit volcanic rock. I say all this because you may have to use raised beds for vegetable beds to work well, which is also difficult in the desert without proper protection from wind and afternoon sun.
