I will soon have a vacation home in a hot climate with no power other than solar. It really saves on batteries if one can use power in the day and coast through the evening/night. AC plus some passive thermal mass should work reasonably well if it is over-cooled during the day. But cool walls at night don't help with humidity - they make it clammy. So is there the equivalent for moisture? Ie, something like bentonite chips or plaster that can be over dried and then absorb moisture later?

AC using ice storage could supply cooling and dehumidification, but I suspect that it is overly complex. Using either solar heat or AC waste heat to actively dry/recharge a desiccant might work. But something passive would be easier.

Radiant ceiling/floor cooling has been shown to be very effective in hot, non-diurnal temp climates. To remove moisture from the air you either need to expose it to something that is at a lower temp than the dew point or use a material having hygroscopic (desiccant) properties. The new InfoSys building in Hyderabad, India used this radiant cooling approach and a desiccant energy recovery wheel in a DOAS AHU. Half of the building was this radiant cooling approach and the other half was optimized VAV...and this is currently the world's largest HVAC side-by-side comparison.  Two years of operation showed that the radiant cooling approach used 34% less energy than the optimized VAV.  An interesting "lessons learned" is that the living space dew point had to be kept below the chilled water supply temp, NOT the slab surface temp, in order to avoid having water vapor diffuse through the concrete slab resulting in water condensation within the slab creating a moisture problem.  There is a nice write up about it in the May ASHRAE Journal.