For american rotation i would expect tail rotor in right sidewards flight to be more efficient than in hover. This increases the mass flow rate through the rotor, so rotor requires less change of momentum for the same thrust. Power goes up from increased airflow mass, and increased thrust required to overcome drag, but actual efficiency is also going up. Besides that extra thrust means Ct/Sigma is getting nearer the magic 0.15 mark as blade AOA approaches max Cl/Cd before stall.
Left sidewards flight has to get through VRS where tail rotor efficiency will be least. Then windmill brake state provides power back into drivetrain to main rotor. Here though the vertical stabiliser drag will actually help you.
In addition there is the transverse flow inproving main rotor efficiency, as Nick comments. This will also benefit tail rotor in forward flight. Non of this includes tail rotor direction making use of main rotor downwash for free thrust.
Dave, you should concentrate on tail rotor power when outflow is equal to left sideward flight velocity. Even so, i'm betting that your "wasted" power in this worse case is still less than 10%.
Besides, apart from for videos showing the impressive sidewards flight capability of a low observable attack helicopters, how often do you cruise sideways?