The mystery is still unsolved but I have some new ideas.
Similar question: does settling happen in phases? I'm starting to think my problem is related to movement of the cables. I had already read about the well known fact that vibrations reduce sound quality, so I made sure that the spikes under my speakers are all touching the ground (well, spike shoes) equally. Next I put my amp and DAC on sponges, which gave a much bigger improvement than I expected. It was immediately noticeable. Then I placed the speaker cables on simple homemade cable risers made out of sticks. Most people do that so it must be a good practice. I just want to rule out any possible causes.
So even if unrelated, at least it helps to isolate equipment, or does it? I somewhat doubt whether the sponges caused the change, or just the fact that I moved the cables. That's because thus far I have always noticed that immediately after connecting a cable, the sound is at least okay and then changes for the worse (sharpness). I have noticed this with all speaker cables, even with the cheapest of cables and speakers.
I have paid very close attention to what exactly is happening to the sound since 6 days ago, which is when I last touched the cables. High frequencies are too loud, but that's definitely not all there is to it, because it can not be corrected with equalizers (I tried, using the program equalizer APO for windows). There is an aggressiveness to it, even in the lower frequencies, but it's more annoying in the high frequencies. It kinda sounds like the cables resist changes in volume, which makes fast sounds like bells remain at their peak volume for too long. As the peak is supposed to be very short, it makes the sound way too loud. It also works the other way around: attack appears slightly delayed, as if the cables resist the volume going up.
In addition to what I described previously (harsh, bad imaging, no microdynamics) what is also typical is a lack of warmth in the bass. Bass is there and can be loud but it doesn't fill the room. Also the bad sound is forward. When the sound is good, everything appears to be more in the background, further away.
How the sound changes: I have heard multiple times a very high pitched screech (probably inaudible to older people), immediately followed by an increase in clarity. It may be a big increase or a small increase, and I can confirm it does sometimes (always?) affect only one channel. After that the quality slowly becomes worse again, and the cycle repeats.
It won't be long before I give up with these cables, but since the vibration adjustments there has been a general trend of improvement. If it takes much longer I will revert to my cheap cables and then it will be interesting to see if any variation occurs with those over a longer period of time. I'm still pretty sure it's related to the cables because I have tried two amps, and I can 100% rule out the DAC and interconnect because I can switch the DAC without touching the equipment (from my audiolab DAC to the one integrated in the amp).