At -40C, the COP is only going to be 1.4. A natural gas fired cogen plant is 60% efficient so even without transmission losses this ultra complex arrangement is

At -40C, the COP is only going to be 1.4. A natural gas fired cogen plant is 60% efficient so even without transmission losses this ultra complex arrangement is not more efficient at generating heat. You are conflating the efficiency of generating mechanical energy (where such arguments hold) with generating heat.