NREL says 1020 Btu/ft^2 of sun falls on the ground and 1550 falls on
a south wall on an average 53.6 F January day in Phoenix, so a 16'x16'x8'
tall greenhouse would collect 368K Btu of sun. Distilling 10 gallons
of water at 1,000 Btu/lb leaves 368K-83K = 284K Btu. With 600 ft^2 of
R1.2 surface, the greenhouse conductance would be 500 Btu/h-F, so 284K
Btu could keep it 53.6+284K/(24hx500) = 80 F (27 C) on an average day.
With an outer layer of plastic film over 4 outer bows and another over
4 inner bows and a vent at the top to let warm moist air enter the spaces
between the layers and condense water into east and west troughs on the
ground made from folds in the outer layer, and a vent in the inner layer
above the troughs to allow the air to recirculate...
If 80 F air enters the top at 100% RH with wt = 0.0226 and 53.6 F air
leaves the bottom at 100% with wb = 0.0088, distilling 10 gallons in
24 hours requires 24x60C0.075(wt-wb) = 1.48C = 10x8.33, so C = 56 cfm
= 16.6Asqrt(8x(80-53.6)), for an upper vent area A = 0.23 ft^2, eg 3 4"
holes. The inner films might have 3 2" holes near the ground.
High winds might be a problem. I expect most tent type structures
wouldnt deal with that. But without knowing the weather conditions I
might be off.
But I agree with your thermal take on it, I do think some form of
shade would be most helpful, not only for the house but also around
it. The 2 challenges are cost of construction and high wind survival.