Plasti-Dip looks interesting. Is it a viable heatshrink-equivalent (for hard to reach places)?
I improved the situation some. Not perfect, but better than the first attempt. I didn't check what helped more (if at all):
2 layer of transparent nail polish/sealant on the inductors. Not sure what's it made of, but plastic didn't like it. The PCB survived.
I chamber the inductors, around and on top, with a plastic foamy packing material sheet. It's quite stiff, and somewhat thick. I added some cotton wool inside the chamber.
Two small transformers got the same chamber treatment, sans cotton wool. I couldn't quite pinpoint the noise source, but maybe they contributed too.
BTW, the noise appears to be harmonics of 1kHz that come and go to a certain degree, plus a stronger and constant ~13.2kHz. I'm not sure if I can infer that there are at least two noise producers.