The rotor coupling response suggests behavior more like a rate gyro, at least in the machines I’ve been exposed to with reasonably broad maneuver envelopes. The S-67 was an interesting example. It did have the electronics from the CH-54B Skycrane installed, but flew so well without ( it did always have the stick force per G, Feel Augmentation System on ) that we never set up the gains and it remained N/A.
During the demo tours in the USA ( 1971 ) and UK/Germany/Iran/Greece ( 1972 ) probably 2-300 pilots got to fly it, and the standard flight included a split S and a roll: one each by the SA pilot flying with the guest pilot on the controls and one each by the guest pilot with the SA pilot helping as needed*. Roll Procedure was simple: put the nose down 10-15 degrees ( any angle ok-just hold that pitch attitude, then set collective around 70%Q ( anything around that was fine ) when you got to around 170KIAS pull the nose up to around +15 degrees-again, anything around that was OK, and when the speed dropped to around 130-140 or whatever, put the cyclic on the right stop**, and watch the world go around. No need to move anything until the world was level again. Roll took about 4 seconds plus a bit and the aircraft would, without any longitudinal correction, come out about level. So, with that 12 inch flapping offset main rotor, the coupling was absolutely there, but easily manageable.
*One of the gust pilots in Germany was former Luftwaffe Chief of Fighters Adolf Galland. He needed no help doing anything.There was one UK Spitfire WWII pilot of high rank and multiple decorations whose name escapes me now, but who walked very unsteadily with a cane up to the 67, and needed help from two people getting into the 67 front seat, but once there, like General Galland, needed no help in maneuvering the 67..
**And yes, we did rolls to the right only, but not for any aerodynamic or dynamic coupling reasons but because in left rolling maneuvers the tail rotor edgewise stresses were high enough so that we would have to cycle count the maneuvers if we went the other way ( tail rotors had a flapping hinge but did not incorporate a drag hinge ).
This post is a bit off subject but indicative that the coupling induced higher rate maneuvers are handled naturally by the pilots.