Max range airspeed is only valid in a no-wind situation. If you're going into a headwind, you want to go faster (you'll spend less time being affected by the headwind).
As far as beeping the rotor - power equals torque times RPM (times some constant, which is of no concern for this discussion). Fuel flow relates to power, and not torque.
If the rotor is more efficient at a lower RPM in the cruise, then you will be using slightly less overall power. Not sure that you could measure that in most helicopters with the accuracy of the torque and rotor RPM gauges - best way to tell is by N1 and TOT changes in my experience.
Altitude will make a big difference if the winds are the same - in the 212 (UH-1N) I used to fly the fuel flow went from 600pph at sea level to 500pph at 10,000' - that's a 20% decrease. There's a good reason airliners fly very high!
Look at sideslip as well if you can - zero sideslip should improve range over the 3-4 degrees inherent in most single rotor helicopters.