I think it is going to be a wash either way. I am very familiar with John Haits work and I think your idea would work very well. However, RMHs are notorious for burning out. Do you want to have to open up an earthen wall to do maintenance over the years? I also think it would be very difficult to manage as far as what time a year you were firing off the RMH to heat load the walls so that the thermal flywheel is kicking in at the right time. You may end up with a steep learning curve trying to strike a balance between comfort, efficiency and convenience. Haits idea was to thermally load the earth by keeping it dry, but the heat came from people just living there along with some passive
solar. I would be inclined to centrally locate the RMH in the house and run a PEX based heat exchanger in the periphery of the RMH to be able to control where you want your heat to go. That way if you have temp monitoring like Hait did, you can see if you are pumping too many BTUs directly into the outer walls. Otherwise, you can radiate and distribute heat via the floors which will not only make things more even, but also increase the area the heat is applied to. I am playing around with a lot of similar ideas to yours, so I'd love to bounce ideas back and forth. I think a hybrid system is what I am aiming for. I want to be able to combine geothermal groundloops, RMHs, "hot" and "cold"
water reservoirs, and evacuated tube
solar heat to make something similar to what you are after. I envision an
underground home with a little more control over the hot and cold and zone heating/cooling.