Finally a breakthrough AnFI.
I used a concept from lecture 2 rotorcraft.
Then again you quoted an equation from lecture 1 aerodynamics, so it seemed appropriate.
But we make progress because you now acknowledge that BET is a fundamental concept in rotor blade design. BET gives an equation that has both RRPM squared and RRPM terms. So when you say "how wrong are you?" the answer is "completely." When you chose to "cancel rotor speed squared" you appear to have left a variable based on rotor speed. So your theory is not "independent of rotor speed" as you so clearly stated.
When it is that simple why go further? We could of course introduce forward flight and resolve the different demands on advancing and retreating side. We could introduce tip effects, perhaps play with some vortex wake models. I could task some BEM work ... but then why bother? Something academically accepted as fundamental, admitted by yourself, contradicts your assertion.
Remember that you brought in your ability to extract the Apache's speed from the video in sufficient accuracy to support a calculation of g to one decimal place in order to support your theory.
Your explanation as to how you can use the background as a reference when it is moving at an unknown speed through the frame and is at an unknown distance will not pass the red face with anyone who has tried to optically track targets.