It's not uncommon for vintage 6SN7's to be microphonic, or to become microphonic. There was a post here not long ago by Kevin Deal of Upscale Audio, who is a particularly knowledgeable tube seller, attesting to that with some rather striking statistics.
A commonly used means of checking for tube microphonics is to VERY GENTLY tap each tube with a pencil eraser, while the system is powered up, and see what you hear through the speakers.
What adds to the puzzle in this case, though, is that the ringing sound is present even when no signal is being put through the system. And even when the volume control is turned all the way down. So if microphonics is the root cause of the problem, the question is what is stimulating the microphonic effect.
Assuming the preamp does not appear to be exposed to any source of low level vibration, I'm thinking that what may be occurring is that a feedback loop formed by the preamp, the power amp, the speakers, and an acoustic path from the speakers back to the preamp may be breaking into oscillation. Similar to what happens when the gain on a public address system is turned up too high and the output of the speakers feeds back into a microphone that is being used.
If that is what is occurring it could very well help to interchange + and - at the outputs of the amplifiers, or at the speaker terminals. Oscillations resulting from feedback are sensitive to phase. If you try that and it does resolve the problem, you could restore the system's overall polarity by interchanging the + and - connections to the phono cartridge, for each channel.
I note, BTW, that your preamp inverts absolute phase/polarity, while your power amps do not. If the phono stage is non-inverting, it would mean that if you already don't have + and - interchanged somewhere in the system, such as at the amp outputs, it would be preferable to do so.
A couple of other points, unrelated to all of that: Make sure that there are no wall wart power supplies, computers, or other possible sources of high frequency interference near the preamp. And try turning off any dimmer switches, fluorescent lights, and compact fluorescent lights that may be anywhere in the vicinity.
Good luck, Marek. Best regards,
-- Al