I took a look at the documents on the hifiengine site, they are similar to what I had already found, and there is indeed a similar spring in the door part, but it is much stronger and has multiple spires.
I'm starting to wonder if it's not actually a spring from something else that somewhat ended up in the device when somebody else did the maintenance, because I managed to reassemble all the parts, everything functions just fine, all that remains now is some occasional noise that seems to be related to some contact issue somewhere with the record switches.
In case some people want to see what it looks like inside, I made a video yesterday:
https://www.youtube.com/watch?v=zMkc9PHOfY0