So the replacement chips arrived and I went to work.


After desoldering the old one - which was actually a TP7660 not an ME7660 (has the same function and is pin compatible) - and soldering a new ME7660 in its place I discovered...
I've never had the IC itself generate significant noise, its always the capacitor or inductor.
That said there are tons of 7660 clones, likely with varying frequencies/rise times/etc. So you could swap that out, or swap the caps out as mentioned.
that you were right, the noise was still there and not a bit less loud. I also found that...
Maybe try to resolder all the SMD componeds there and the chip to see if something change.
this was a good suggestion, too. The old chip had a cold solder joint (on the output pin) that was clearly visible when I lifted it.
I don't have the necessary 0805 10µF capacitors here but I have some electrolytics, so I tried those.

Looks terrible but it works, sort of. The noise got a lot less loud but I can still hear it. So one of the ceramic capacitors was involved (both were about the correct capacity), but there's at least one still producing unwanted sound.
Since I don't know which I would have to desolder each one, measure it and order a replacement. That's rather error prone, does someone know the right values?
Also which ceramlcs are less likely to produce such noise, is there a brand were this doesn't happen as a matter of principle (or quality)? The two through-hole caps will be replaced too, once I found the other culprit(s).
Before all this happened I also discovered (under the microscope) that the TP7660 apparently was hand soldered and so was a second capacitor on top of the 1206 to the right of the chip. I didn't notice that in the earlier pictures I had taken. So this was not a new unit but a returned one with a failed repair attempt, great.

Not sure how to determine the intended capacity of the stacked cap, the value that my LCR tweezers spit out likely are not what it is supposed to be.