There is a reason why 3D rendering is difficult; light bounces an awful lot. Objects slightly tint the whole room even if unperceptibly. Lamps vary in intensity, and their shape affect the outcome. So how do you even set the scene up? With a small card the phone being so close can affect lighting. A distant large surface requires more distant lights for uniformity, o simply more lights. Getting the camera out of focus might be useful, but can't correct large scale phenomena properly. Getting the watermark is the difficult part imo.
After all that, once you substract it from every picture you take, every subtle mistake you made in the watermark generation phase will become your new watermark. You bet your privacy on your error being very close to the zero function across the whole grey card. As mentioned in every other comment, astronomers do these calibrations often... for a living. I'm simply not that invested beyond removing EXIF data.