Yes there is a reason for the increase in rotor rpm when increasing the load factor on the disc in maneuvering other than coriolis effect. The best way to make sense of it is: say you are in auto rotation. As you are gliding down if you could some how add weight to the aircraft the rpm would increase and you would have to start pulling pitch to keep the rpm constant as you take on weight. As you loaded a larger amount of weight you would get to the point where your collective would be pulled pretty high. Adding weight to the helicopter is basically the same as increasing the load factor by turning or pulling aft cyclic. Increasing load factor in power on flight does the same thing to rpm as it does in unpowered flight. RPM does not increase just because of coriolis effect. Coriolis effect only increases rpm for the time when the coning angle is increasing, once the coning angle stabilizes there is no more coriolis effect and the rotor still must overcome the same amount of drag as before the coning was increased if it is to maintain rpm. If coriolis was the only force trying to increase rotor rpm, then when you rolled into a turn torque would momentarily decrease and once you were stabilized in the turn torque would return to where it was. We pilots know this does not happen.
Now for the explanation. It will help if you dig out a helicopter book that shows the airfoil section of a blade with all of the lift and drag vectors. They should show one for powered flight and one for autorotation. If you look at the one for autorotation you will see that the total force vector is perfectly vertical. That means that there is nothing opposing rotation and nothing to increase it. Now look at the diagram for powered flight, you will see that the total force vector is tilted aft trying to slow the rotor down. The torque generated by the engine of course overcomes this. Now imagine what happens to the relative wind vector if you increase the load factor. It will become more upward actually increasing the angle of attack. But look what happens to the total force when you change the relative wind.
Remember the drag vector is always parallel to the relative wind and the total lift vector is always 90 degrees to it. The total force is the lift and drag added together.
So if the relative wind is more upward then the total force is more forward, whether it is powered flight or unpowered.
Bottom line: when you increase load factor at any collective setting, you change the relative wind to be more upward and that angles the total force forward which is a decrease in drag and rpm increases or torque is reduced in a governed engine.