But a gas burning furnace can have 100% efficiency, that is trash compared to what I get from a heat pump considering a gas power-plant (60%) * national grid ef

But a gas burning furnace can have 100% efficiency, that is trash compared to what I get from a heat pump considering a gas power-plant (60%) * national grid efficiency (90%) * heat-pump 500% efficiency where I am (combined efficiency around 270%, or 2.7 times the gas furnace). The only gas-based solution to get close would be using a gas generator at home (30%) to power the 500% heat-pump, and routing the 70% of waste heat inside (to get a combined 220% efficiency). But that heavily depends on the heat-pump efficiency, which will depend on your ambient heat and instalation.