This seems really clever -- kudos!
I'm curious how it actually works?
At first I assumed you were comparing the vinyl track to the reference digital track from some streaming service and either analyzing the frequencies with FFT or the timing of peaks.
But I watched your demo video and you don't need to tell it anything about the song.
Which makes me think you're rather doing an FFT and simply trying to match how well the frequencies align to the well-tempered scale based on A 440 hZ.
Which then leads me to three questions:
1) Obviously this wouldn't work if you were playing a standup comedy album or something? Or the drum solo part of a song?
2) Are essentially all albums perfectly in tune with A 440 hZ? For example with classical music, I understand that 442 is also used, baroque is sometimes at 415, and 432 has been common as well? I don't know about pop but I can't help but wonder if some artists have intentionally chosen something other than 440 over the decades.
3) I assume this won't work if the turntable speed is off by more than 2.8%? Since the distance from A4 (440 hZ) to A-flat-4 (415.30 hZ) is a decrease of 5.6%, and so if the turntable is off by more than half of that you'd be trying to align to the wrong note?