I called my electric company to see how their rates work. I'm paying $.039 per KWH off peak and $.081 per KWH on peak. The off peak rate only applies to the furnace when the power company is at low demand. So I still have to be careful about leaving lights and appliances on.
I wonder if that is accurate info. For it to only apply to the "electric furnace" then the power company would need two meters one for the electric furnaces and one for the rest of the house. Not saying that is impossible but it is unusual. Not sure why the power company would care. The lower off peak rate is because they don't have enough demand off peak and are trying to stimulate demand. A power company interested in their bottom line wouldn't care if you were smelting aluminum off peak as long as you are doing is off peak.
If that info is accurate then you only get lower rate for power used by the furnance. Thus while a mining rig would be just as efficient it would cost more simply because it is billed at a higher rate. If it were me I would callback and reverify that off peak rate only applies to electric furnace.
If it DOES then replacing your resistance heating "furnace" with a high efficiency heat pump could reduce your annual heating bill by 50% to 80%. If you also have an AC the heat pump would replace that too and likely at higher efficiency. If your AC is more than 5 years old it could cut your cooling costs by 20%-30%.
Still even your peak rate is very cheap (if that is total cost including transmission) which partially explains why your home is still using higher cost resistance heating.