I guess the amount of water produced by these stills depend upon how much humidity is in the air? In summer our humidity is generally in the 10-15% range. Will one of these stills produce much, if any water at low humidity levels?
Yes.
The solar still with the plastic sheet over the hole will produce water based upon moisture in the ground.
Ways of increasing productivity in an extremely arid environment include placing pieces of plants in the hole, pouring urine and/or fresh blood into hole (before you seal it up), and digging the hole in a low-lying area like a dry stream bed.
As I indicated earlier, do not pour radiator antifreeze/fluid into the hole. People might be tempted to do this if their car broke down in the desert, but--as someone with HAZMAT certification and a degree in organic chemistry, as well as having volunteered at a poison control center--this is extremely dangerous.
Ethylene glycol can evaporate out and condense along with the water, and this will poison you by destroying your liver and kidneys.
Likewise, don't set up a solar still near a road where car exhaust may have left a residue in the soil.
Certian places in the desert may also be a problem, as there are old mining areas that have residues of arsenic, cyanide (used to process gold and silver), lead, and mercury in the soil....so I would avoid digging a solar still in such areas.
This seems like a lot of restrictions, but it really isn't. If you use sound judgment, you shouldn't have any problems. If you don't have sound judgment and common sense, then all the solar stills in the world won't save your ass anyway.