Have you considered a "Heat Pump"?
At first glance they look good
but then you realise they need a pipe
and only seem to cool the home, not heat it. They seem to pump heat out not in. I suppose you could put the unit outside and have it pump the heat in?
So yes the heat pump is likely the most efficient way to heat/cool the home, but I would guess really not looking at how efficient but how cheap, I see no real reason why we could not have a petrol/TVO engine running a heat pump, at one point you could get a gas boiler with a sterling engine built in, but we are not really looking at efficient methods, but cheap methods.
The problem with the heat pump is in the main they want to run cooler than traditional water distributed methods of heating, so radiators either need to be bigger or fan assisted, fan assisted is likely the best as then can heat and cool, but to cool need a method to remove the condensate, so need pumps and drain pipes, which adds to the expanse.
The pipe on my tumble drier is very small, so it can be done, but there seems to be a lack of self contained heat pumps, there were at one time units that hung out the window, but not seen them in years.