This is eye-opening! I have some noise coming from mine, so I'm definitely going to do a thorough cleaning of the sockets, and take a look at the exposed contacts beneath the base plate as well.
I'll add that part of my noise issue is coming from a neighbor with a very serious ham radio setup, including a 30 foot transmission antenna in his back yard. It seems that V1 and V2 are very sensitive to microphonics and RF interference. Just walking around the room can change the way the interference sounds, as my location can either block or magnify the signal. Very strange stuff. I was able to eliminate 75% of the sound by forming some aluminum foil around the tube area, so I think I'll be pursuing a cleaner and more complete solution in the future with an actual Faraday cage.