[morzh]

Just hooked the GND wire to GND in my outlet. Same thing, nothing's changed.

Well, I just paid a bit more attention. With or without GND connected there is a change in volume.
The problem is that where it would be an acceptable volume level while listening to the loudest station, this is where that bald spot is.
So the volume stays very loud, and then goes to almost nothing. But it does change.

I have to tune out a bit, and thus make the station less loud, and then the volume regulation works better.

But...still a new regulator would be better.