The impact on coming angle and conservation of momentum is a transitory effect, rather than a steady state effect, so not relevant in this case.
ie, if you suddenly pull G and effectively increase your weight, the sudden increase in lift required from the blades will cause a coning angle to develop thus increasing Nr due to conservation of momentum.
That is not the case here.
Here we are flying 2 identical helicopters except one weighs more than the other and entering Auto.
The heavier helicopter is already producing more lift to remain airborne and balance it's weight, so already has a greater coning angle therefore no sudden increase in Nr due to conservation of momentum.
A heavier helicopter requires more lift to remain in a steady non accelerative state such as Auto.
The only ways to get more lift from an airfoil are to increase airflow or angle of attack.
In this example we have limited ourselves to a steady Nr, so we are left with angle of attack.
If, we were to believe that an increase in weight leads to a decrease in ROD as per the premise being discussed here, we can see from your diagram that there would be a decrease in rate of descent airflow which would then lead to a decrease in blade angle of attack.
It just doesn't work.
The way to test any theory is to take it to extreme.
Does anybody here really believe that if you added a million tons to a helicopter it would fall more slowly?
Or conversely, if you attached an enormous helium balloon to the rotor head we would plummet in auto?
No, our internal newtonian physics professor can spot a flawed theory quite well.
In reality, as you increase weight, the ROD will increase, and to minimise this you would have to allow the Nr to increase to stop the stalled portion from growing to encompass the entire blade.
There will be an optimum increase in ideal Nr with increase in weight in auto.