I had this problem for years and years, it makes you want to pull your hair out and start playing the banjo.
I have various and amps and guitars, and it was actually a combination of issues which made it very difficult for me to isolate simply by switching gear around.
The Main Priority is the pre-amp tubes, i'd still buy some more and play around with those, theyre not expensive and you always need spares.
My problem was a combination of dud pre amp tubes one set of microphonic pickups- you can get these repotted easility, cheap dodgy cables and vibration of the pickups.
Also it can be the mains you plug your amp into. Try using it in a proper practice room to see if this has any effect.
Are your pickups screwed into the body or attached via guards? If they are attached via guards you may be experiencing a viabration of the pickup causing oscillation. Although this does seem like a long shot if you have the problem at low volume. Easy way to check is to hold your pickup steady and see if the noise goes away.
Still it does sound like a valve issue, dont belive the BS about the volume, Unless youve got the gain right up and your overloading the FX Loop, i would of thought that wouldnt be an issue.
