Sure but the problem remains: you can't do that with only a few oscillations of a weak signal against a loud noisy complex signal.
You simply can't detect an inaudible-to-human-ears 0.5 hZ signal from 3 or 5 seconds of complex normal-volume audio, down to the accuracy of cents, much less 0.1 cents.
As I said above: a 1,000 hZ signal? Absolutely. But a 0.5 hZ signal? Absolutely not. There just isn't enough signal for that level of precision. No matter what tool you're using.
But you could easily detect frequency modulation of a 220Hz signal by a 0.5 Hz sin wave, which would have sidebands separated by 4 cents. This is conceptually similar to heterodyning. Wow in the source material ends up creating sidebands of the source material in a frequency range that is more amenable to signal analysis. Whether this works or not depends on how much wow an actually record player has. But a back-of-the-envelope calculation seems to suggest that very tiny amounts of wow should create detectable side-bands.
My suspicion is that OP assumed that the source material was accurately tuned to A=440, which is not a safe assumption, but is probably true for any source material that has a keyboard instrument which will almost always be tuned to A=440. Calculate the reference pitch for the source material, and you can tell how much the speed of the turntable is off. (And as others have pointed out, may be completely buggered by common mastering practices, and by Original Instrument recordings of classical music using pitch references other than A=440).
But it doesn't seem implausible that you could use analysis of wow in the source signal too.
You simply can't detect an inaudible-to-human-ears 0.5 hZ signal from 3 or 5 seconds of complex normal-volume audio, down to the accuracy of cents, much less 0.1 cents.
As I said above: a 1,000 hZ signal? Absolutely. But a 0.5 hZ signal? Absolutely not. There just isn't enough signal for that level of precision. No matter what tool you're using.