Everywhere at any point on this LP, the 1000Hz test tone has been encoded by a perfect cutter lathe. In practice, the stylus tip is just a point on the surface of the LP; it doesn’t "know" where it was a fraction of a second before or after any particular event. How can this phenomenon change the fundamental frequency?
Exactly, @lewm. And the answer is that it can’t change the frequency. We know that because the Fourier Transform proves why a little squiggly groove on an LP, or that same wave magnetically transferred to tape, or a binary digital code, can represent the sound of a full orchestra, and get the frequencies (pitch) correct.
What could affect frequency would be if somehow, on playback, the overhang changed. I can’t imagine how that could happen.