I too have done calculations on my three sources of heat, which include a 10 year old heat pump which operates to 27 F at which point it starts to do defrost cycles, LP which is burned in an on-demand boiler and provides in-floor hydronic heat in the basement and blown heat through a heat exchanger in the furnace, and a wood stove in the basement burning fir, for days I am home. Using last year’s numbers, the heat pump is cheapest, followed by propane, but if I’m home and the temp is below 27 F, I’ll make a wood fire. There is a real cost for wood, as I sometimes bring down a dead tree, but mostly pay the equivalent of $210 USD for a cord of split fir delivered but not stacked. I also have a propane fireplace but use it for ambience since my condensing boiler does a better job of distributing heat. Having said that, the propane fireplace and wood stove both work during our power outages that happen in this rural area.
My American Standard heat pump has been trouble free for 10 years except for a condenser I had to replace. My 10 year old Viesmann boiler however needed a new fire tube, new gas valve, new computer controlled fan, new ignition cord and several ignitors and new face plate for the chamber that was warped. Total was about $2500. The Regency fireplace still has the original fireplace bricks and burns hot and clean, exhausting through a double insulated stainless steel chimney vent. I find the gas fireplace thermocouple has to be cleaned once a year for the piezoelectric igniter to work.