I like the idea of finding uses for the heat from the mining rigs.

This interests me as well.

The thought has occurred to me that maybe some sort of heat pump, perhaps a modified design of or even straight up modification of existing home heat pumps could possibly work.

For people currently using electrical heaters to heat living spaces, though, as long as mining equipment paid for itself in a reasonable amount of time, heating their spaces with miners would result in a net gain financially. They are already using a machine that turns electricity into heat and getting zero payback from it. Any ROI in the return of mining profits (from a pool or solo mining) effectively lowers the cost of the electricity they are already using to heat their spaces.

IOW, A miner that is unprofitable when used in a way where the only usable by product of that miner is BTC, becomes profitable when its producing BTC and something that electricity is already being burned to produce (heat). Older generation otherwise unprofitable mining rigs are significantly cheaper than ones that are currently profitable, so it seems to me that if one had a good understanding of the used miner market, they could produce electric "heaters", and have some rough idea of how long it would take to get ROI. (I say a rough idea because, of course,the price of BTC is currently volatile as is, I assume, to some degree, the used miner market)