I also live in NC, and as a mechanical engineer, I have insight into HVAC issues. Thermal mass is great anywhere, all the time. If you have enough you can run your air conditioning during the night. This is good for two reasons. During the night, you will be rejecting heat from your house at at lower temperature, so the pressure in the heat pump's condenser will be lower, and the compressor's motor will use less power. Night is also off peak, so if you have time of day rates kiloWatt hours are cheaper.
I would have a timer set, so that the heat pump would start at such a time so the target temperature would be reached about dawn. That way the outside temp would be as low as possible.
Sufficient thermal mass would make it unnecessary to damp a wood stove at night to keep it burning. You could run it wide open until you reached a target temperature, and then just shut it down.
The problem with solar chimneys, earth tubes, and the rest of the unpowered ways to keep cool, is they do not deal with humidity. Today, vapor compression heat pumps are the only technique available to homeowners to dehumidify. All dehumidifiers available commercially are actually heat pumps.
If you want to air condition as responsibly as possible, look into a ground source(often called geothermal) heat pump, and some photovoltaics to help power it.
I want to build a home with CEB load bearing walls, and non bearing straw bale walls for insulation. Between the thermal mass of the block, and the insulation of the bales it would take days to get cold in the winter.
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