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Having one channel shielded (I assume from the function switch to the 6AU6 grid) and the other not shielded is definitely a hum issue. Does the hum you hear come from the unshielded channel? Or both, equally? If the latter, we're talking a power-supply issue most likely.
From the volume-control wiper to the 6AU6 grid, you say you have a 220K resistor to ground as well. That's a good idea, actually; should the wiper go open-circuit, without that 220K resistor the grid would float and cause the tube to operate erratically at best (go into runaway at worst).
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Haven't checked for sure, but I do get the distinct impression that the hum is coming from one speaker, not both.
I've got plenty of shielded wire floating around in my parts box, so I'll replace it anyway. The hum is only noticable with the volume at or near max, so the power supply is doing a very nice job.
Regarding the volume control, the 220K does indeed serve to make the pot a log-pot instead of linear. Doing it this way is far cheaper, since log pots are more expensive. I'll have to replace them, since the readings at the same setting are different for each channel... and probably contributes to the balance issue. (and it's practically impossible to get an accurate reading of resistance with things in parallel and the uncertainty of a variable control!)
Edit: Yup, the 220s were out of spec. Replaced them and now the balance is equal on both sides.
You mentioned the loudness tap; this explains why at about 1/2 the control, the bass suddenly jumps up in volume... Suggestions to fix? The 47K resistors seem to be within spec.