SASless,
Having done 1000's of engine cuts in critical flight conditions, I can say with great experience that the behavior with cyclic vastly controls the rotor decay.
A little back stick does help swap airspeed for rotor rpm, as well as help hold the nose up when the collective is rapidly dropped. If the aircraft rolls off to one side during the initial cut, it is far better to let it do so (within limits) than to use strong lateral cyclic, which consumes power and makes the rotor drop even faster.
BTW the back stick loads the rotor (increases thrust and g) but in this case that is ok, because it increases the autorotative flow a bit. The one case where it hurts is at very high speed near or at Vne while heavy and high altitude. If you are near stall, back stick makes the stall factor rise, and the rpm droop can be very big.