> If you expressed the efficiency as "2 joules of heat moved per joule of mains electricity consumed" you eliminate the canceling that would let you phrase the ratio as 200%.

But that's the performance. Efficiency is usually a measure of how good the performance is.

In this case there's a practical reason not to call it efficiency, because there is a well understood maximum performance which is the Carnot limit, so for practical purposes (to avoid confusion) PumpedHeat/Power is called "coefficient of performance"and CarnotLimit/PumpedHeat is called "efficiency", and it has the usual properties that it cannot exceed 100% and it measures how well your system works in a more or less absolute sense.