Assuming the record is travelling at constant speed, then the motion of the stylus forward and back relative to the line must alter the apparent speed, as seen from the record groove, albeit minuscule.
You are really confused.
Your fervour for FFT analysis appears to be an impediment to understanding basic maths and physics.
You are really confused. I’ve never, ever mention FFT analysis. You’re apparently confusing FFT analysis with the Fourier Transform, an indicator that you’re having issues with your "basic maths."
The Fourier Transform is the theorem which explains how digital and analog audio work. It also disproves your fantasy that phono cartridge tangency affects frequency. As I’ve mentioned, I can also disprove your fantasy by measuring the frequency of a test tone as it’s played from a test record. It’s not difficult to do.
Of course, you’re free to imagine and fantasize that you’ve found some flaw in the Fourier Transform. A Nobel Prize awaits you if you can show you calculations. Good luck with that!