Aakee - I believe the charts and study you refer to are meant to prove that in order to achieve minimum RoD in autorotation, you must vary the speed depending on AUM.
It seems to show that min RoD is achieved at a slightly higher (than bucket speed) forward speed at high AUM and slightly lower speed at lower AUM.
The rigging charts show that for a given rigging setting for minimum collective pitch, the lower the AUM is, the lower the acceptable Nr in auto is - conversely, the higher the AUM, the higher must be the minimum Nr achieved.
In a vertical autorotation at steady Nr, the only way to further increase that Nr is to increase the RoD and that is what would happen if you suddenly increased the AUM.
Higher AUM = fall faster = higher RoD and higher Nr. Because we have Nr limits, you will contain the Nr by raising the lever. is there any change in steady state RoD at the same Nr between high and low AUM? - never seen a graph to show it but happy for you to prove it is lower at High AUM.
And my copy of Prouty doesn't have the answer - even if there is one it would be a generalisation and not necessarily true for all helicopters given the variation in blade designs and aerofoil sections, even down to the cleanliness of the blades as that markedly affects your profile drag.