There is a free and accurate tool to do this measurement...
That's all fine, but you notice that the posted graphs are for 30 minutes.
There's nothing wrong with that, but in the time we've all been discussing this, somebody could have knocked off the simple scope check that I mentioned.
(i.e. reference 3150 Hz into one channel, turntable into the other channel and look at how the signals slew by each other.)
1 rotation / 33-1/3 RPM = 1.8 seconds
1.8 seconds * 3150 Hz = 5670 cycles
5670 cycles * .1% wow = 5.67 cycles
So with a low figure of wow you should be able to see a gentle slewing.
If you find that things are insanely clean, you could run the test as an XY Lissajous.
I personally would like to see such a scope video.