Yes I understand about the problem of overheating the soil underneath the house. Overheating isn't so much of an issue here because we are about 15 degrees farther north so the sun isn't so hot in summer and because of the gulf stream it isn't very cold in winter, just 5C average in January.
There is a company, in the same county as me, called Viking House who are experimenting with seasonal stores and solar heating and currently they seem to favour large areas of variable output, drain back, solar panels combined with more limited underfloor heat storage.
In the UK there are big subsidies for PV so the development there is tending towards PV powered ASHPs. The end result is to save money and scarce fossil fuels.
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