DB,
Pushing that Single Button...."IAS"....should have been the exact right way to do what the Crew tried to accomplish.
But...my question keeps coming back to why the Crew did not do that and that is where I fully agree with you about it being far more complex an answer than it would appear.
To me....it simply defies logic.....but I think it follows from the Crew deciding to use different airspeeds and ROD's in what should have been a far more stable approach if a single approach airspeed had been decided upon.
Ultimately.....doesn't the "KISS" method of Helicopter flying apply?
Slow the aircraft to approach speed upon arriving at the initial approach fix, then maintain that airspeed to the Final Approach Fix....then if a further reduction in airspeed is desired.....prior to passing the FAF make any other Airspeed reduction and have that airspeed stabilized passing the FAF.....and hold that "Final" speed until completing the Landing Visually.
Changing more than one parameter at a time seems unnecessary if the Approach is planned properly.