A couple of ideas....
There are supposed to be Ammonia / Natural Gas / LP Air Conditioning units. They might be as efficient as running a gas generator to make electricity to run a compressor to run an AC unit, and they should be a heck of a lot quieter. Ammonia refrigeration is the oddest thing, using heat to generate cooling.
I would think that it should be possible to make a solar - Ammonia Refrigeration and AC unit. I did see a description of a solar ice maker, but it was HUGE.
Note, the temperatures at night drop by 10-20 degrees in many communities. If you work all day, open your windows, or put in some fans to blow out the hot air and let in the cool evening air.
Nothing beats some good shade trees.... unless they are obscuring your solar panels or blocking your wind. Consider planting a grove of trees upwind from your house.
I'm not sure about the idea of living in a cave.... however, your basement is often the coolest room in the house in the summer, and can be the warmest room in the winter.
Good Luck,
Clifford