Okay, new result: two puron filters have been in use for the recommended 30 hours. The sound seem to be more immediate, less thin, but the original problem still remains. I don't think there's any improvement at all. It was worth trying and probably still a good investment for later.
So now I'm back to believing it's burn in related.
Thanks for sharing your experience. I can confirm the initial drop off. That one is the worst, not pleasant to listen to at all. All sound comes from a single point in space (for each speaker), and there's a force behind transients, as if it's fired at your ears from a gun. After that it turned into a rollercoaster ride indeed, with good and bad periods, but it never gets as bad as that first drop off. That's just unlistenable.
That makes sense. If there's such thing as "overcooking", then apparently the sounds played affect the behavior of the cable.
If you have any particular strategies I would be interested.
I hate this by the way. It would be so much easier if cables performed the same, always. I'm even more interested if there's a cable that does not need burn in. A possible candidate I came across are the cables from inakustik. They are designed in such a way that the metal wires (copper/silver) touch almost only air instead of plastic. This is relevant for the following question by Kingrex:
That is indeed my experience with cooking. Overcooking made the sound dull. Even white noise was dull. That went away so there's definitely another break in process.
All sources I have found that make claims about how it works say it's the insulation material that causes the biggest problem (settling after bending takes less time). It has to do with static charge. See for example
https://nordost.com/blog/what-is-cable-burn-in/ and
https://www.mojo-audio.com/blog/breaking-in-cables-and-components/ .
What's wrong with the groundmaster?
Changing the wiring in the house may be something for later and only if it's really important. I'm not looking forward to doing that because I'm renting.