Holmz, if you are thinking of how to prove or disprove your frequency hypothesis, I fear we cannot do the experiment in the real world, because we require a perfectly created, perfectly centered, and perfectly flat LP on a TT with perfect speed accuracy, in order to examine the phenomenon you claim exists (and others do too, in fairness). Imperfections in any of the foregoing elements would likely cause a frequency distortion that would drown out the effect you want to detect. Fourier or no Fourier. But we can argue until the cows come home.
By the way, I was thinking that your observation, that you have to rotate the platter by about 20 degrees in order to set the two null points using your protractor, is really a product of how your particular protractor was made. It is possible to imagine another protractor where the cartridge can be aligned at the inner and outer null points without having to rotate the platter at all.