Yes, it's the speed stability. The Linn has a 'waver' to the speed which actually seems to enhance some music but totally muck up other tracks. It's inherent to the design. I love it and hate it at the same time! ;0)
I know you keep pushing this speed stability stuff and I am still not convinced though out of personal interest it is something I am trying to check.
From what I have read the LP12 usually has good wow and flutter figures which is the common measure of speed instability. I have some Hi-Fi Choice mags from the 80's and they always regarded speed as pretty good. The Rega's on the other hand tended to be a little fast but with some slowing under load.
Speed instability is generally measured using a fixed 3000 or 3150Hz test signal. Speed instability will show up as pitch variations which can be measured. For example in this thread at the Hoffman forum there is even discussion about a utility that can be downloaded though I have not tried it yet. I am not aware of any kind of speed instability on record decks that will not result in pitch changes.
https://forums.stevehoffman.tv/threads/wow-and-flutter-measurements.981526/
If speed stability is an issue and audible during normal playback then it should also be audible on playback of a test record using the above tones which are where speed fluctuations should be most apparent. On my LP12s and most other decks I do not hear any pitch changes.
It is possible that speed instability could arise out of a deck with problems such as a belt in poor condition or rubbing, bearing or motor issues or detritus on the belt drive path and these could cause a deck to degrade over time.
The wow and flutter measurement itself can be a bit controversial for example here but most decks give good figures out of the box.
https://www.audiokarma.org/forums/index.php?threads/wow-and-flutter-some-figures.320629/
There are 2 other situations which could lead to a perception of speed instability that I am aware of.
1. Room reflections causing standing waves that can lead to quavering that will be particularly noticeable during the fade out of a track where there is a sustained note. I get this quite a lot because I have a small listening room with uncovered hard walls. For testing purposes these standing waves could be eliminated by using head phones or transferring a digital copy to PC.
2. Off centered and or warped records.
What I suspect is that these may vary between decks depending on the relative clarity of the deck and the tonal frequency response of the deck/arm/cartridge