"An old house with electric heating and cooling could well be what he has." Definitely could be the case. Your situation is interesting in that it is opposite

"An old house with electric heating and cooling could well be what he has." Definitely could be the case. Your situation is interesting in that it is opposite to the order of transitioning towards a heat pump over here. Perhaps a heat pump was your starting point as there was no gas connection? Over here we start with gas heating (almost every house) after which we try to transition towards a heat pump. They say you should first insulate your house to the maximum possible before even considering a heat pump. Fail to do this and the heat pump won't even be able to produce enough. This calculation is of course locally specific, unlikely to apply to you. In fact, many houses will never be able to transition and will end up with a hybrid pump as the maximum achievable.