Update: after discussing this once again, we came to the conclusion that - if the creative goal is to be able to “morph” between a “given color” and “white” using a single parameter - it is (instead of using the above attached Generic RGB+W) better to stick with using a fixture like Generic RGBW and instead of controlling the white modulation directly, choosing the HSL color mode in a Beam device, finding the desired Hue and controlling Luminosity between 0.5 and 1.0 to transition between the chosen color and white.
This way we can keep using Beam’s RGB → RGBW conversion, which ensures the white LEDs are correctly used for representing whites.