I think you are back to where you started. If it was cheaper to use gas to run a heat pump then everybody would just run generators in their houses off of gas instead of using electrical lines.
In MA this actually does work at first glance: a 23% efficient Generac 7171 is rated for 9kW at full output on natural gas, and uses 127 ft3/hr (1.37 therms). This is $0.30/kWh at $2/therm, compared to the $0.323/kWh I pay the power company. If you were doing this for real you'd put in the work to find something more efficient than this unit, which would then be enough to make up for the cost of the generator and the maintenance.
Except it's not legal to do this, and even if it were there'd be a lot of hassle.
I had found some things saying you were limited in how many hours per year you could run standby generators outside of emergencies [1] but possibly this only applies to larger systems? [2]
That has been proposed. Well the proposal was to run a small engine powering a generator, then you cool the engine to heat the house, while the electric is sold (or otherwise powers the house). However modern gas furnaces are > 90% efficient and it is hard to get an engine that efficient for heat (remember the engine will be running indoors so it needs to not fill the house with noise of CO). I think no matter how you look at it, you can't make this system more efficient than just using the furnace to generate heat without the engine.
> I think no matter how you look at it, you can't make this system more efficient than just using the furnace to generate heat without the engine.
I don't think that's right: look at micro-CHP (Combined Heat and Power) systems: they run an engine to generate electricity, and then capture the heat for heating. I don't think you can get them for residential in the US though.
Instead it everyone rubbing their own little power plant. Economies of scale suggests that’s it probably cheaper to centralize that electricity generation in a highly efficient large plant, which brings us back to exactly what we have been found got that 100 years
