Still having these symptoms after all these years.
Got a scope?
SEL49 already marked up the schematic so you know what's what in Channel 1. "Divide and Conquer": Cut Channel 1 in half, and poke the scope probe there first.
"Halfway between the Input Jack and Volume control" appears to the the 0.01µF coupling cap that's the output of the 2nd gain stage of V2. Attach the probe after the cap, and listen for noise. When the noise happens, do you see corresponding squiggles on the display?
- If "No" the noise is happening after this point, and before the Volume control. Divide this portion of the circuit in half, and probe after the 0.005µF coupling cap at the first stage of V3. Check again for display-squiggle when the noise happens.
- If Yes, you will still need to figure out which stage of V2 is making the noise. Probe right after the coupling cap of the 1st gain stage of this channel and repeat.
Once you've isolated the gain stage making the noise, there are 2 or 3 main possibilities:
1. Noisy tube. Hopefully you've already tried a tube-swap
2. Noisy resistor. Could be a broken component lead, could be noise due to DC Volts across the resistor. There is test gear to test the latter, but you could just swap with a new resistor (though you are hoping the new one is not noisy, and would have confirmed that with the test gear). "DC Volts" tends to be more-volts = more-noise, so plate load resistors are the typical problem. If that doesn't work, a cathode resistor could be the noise source since most of these are unbypassed (a bypass would tend to bypass the noise as well.
3. Noisy cap. Unusual, unless a cap lead is broken, or the cap causes popping noises by leaking DC volts.