why did my record player slow down, speed up, then go back to normal?

I am a vast well of helpful information. For instance, you may wanna get your keyboard checked out. Judging by your previous posts, the period key seems to be damaged or get stuck. 

Lee, has this only happened once or does it do this intermittently? If it happens occasionally I second the speed pot degradation theory. Good starting point to check at least 

ET phone home.

Depending on time of day and prevailing weather conditions driving load against the power grid, it might have been a fluctuation in available current in the power grid feeding electric service to your home. It happens on a weekly basis for our power grid. The various fans that help our ancient HVAC system move air in our home will slow then speed up at various times through the day, much too subtle to cause the lights to dim. Once the load stabilizes after 10pm or so all things plugged in are much happier. 

And you think that's all it is then. Interesting.
https://www.youtube.com/watch?v=G554Xa8MElg