I would think that for that use case, using thermal storage should be more efficient? Don't store electricity to run AC later, but run AC to cool down water or the ground beneath your house or something, and then cool your house with that later.
Or build something like an Earthship (http://earthship.com/). I know that these can air condition a house in New Mexico through geothermal heat transfer, however no idea how they handle the more humid summers of the South East.
They work, but aren't as comfortable as in drier climes. Humidity is tough to control with low-energy, low-maintenance solutions. Unfortunately, many people's discomfort perceptions are heavily influenced by humidity.
I recently moved from Nashville (quite humid) to Flagstaff (quite dry) and the difference is amazing. Large temperature swings are barely noticeable in the dry climate, but would require substantial changes in weight of clothing in the humid one.
That would require a huge amount of work and expense, and at the end of the day cold water isn’t very good at cooling off giant masses of air and furniture.
