Hard to say.
The bottom of the board where the pot ground pins themselves come through is accessible, and that ground checks out ok, and if the pot elements themselves lost their connection to the ground terminal, things would be acting quite differently.
There is wiring going off to the loudness switch that could be picking up noise, or the grounding of the volume control board or the loudness board or a combination thereof could have a problem, or the front plate of the chassis itself (depends upon the construction) could have a problem.
A signal ground going to the chassis at the wrong place (not the star point) could also cause problems. As opposed to the "isolated" grounding of the pot or switch bodies.
Shorting 3, 4 & 5 just plain kills all audio coming in after the volume control.
Plus I don't have an idea of the relative level of the hum, and the touching of the chassis and pots affecting the hum puts it in a nasty diagnostic situation.
Compounding that is the fact that the board the volume control is on (switch circuit assembly aws-072) has many many wires that are sensitive to noise coming in, with grounds that are not terminated (on purpose) and the board has a complete system of ground "fingers" between signal carrying traces.
That's why I wanted only speakers and power being the only connections to the unit while testing.
edit: if there are florescent lamps close to where you are working, merely the bottom of the chassis being open and unshielded by the bottom plate could be doing it to you, so you could put the plate back on with all the screws, and turn out the lights in the area as a check. The wooden top of course makes little difference...
I would like you to dial up the hum, and then try turning on and off the tape 1, tape 2, 4ch adapter and NR adapter switches to see how that affects the hum. There are 16 possible combinations... then try two different things with the jacks for them on the back: one is taking a pair of interconnect cables and on each of the four plug sets testing the hum with the outs to ins of that plug set connected together. The other is making a set of shorted RCA plugs and plugging them to the IN side of each plug set.
The tone defeat pop probably calls for a recap of the tone board, it probably is just one channel. Leave the tone off for now.
What I would do now if it were on my bench, would be to make up a "battleship braid ground" - a very heavy, insulated ( to avoid short circuits as it draped around) ground wire with a very stiff alligator clip on one end, soldered to the star ground point on the other end. You can use a 14 gauge wire....
Then I would clip this onto the various suspect grounds we have already checked from the volume control board (5 of them I think) and the loudness switch board, to see if any effect could be noticed. We are looking for "weak solder joints, bad foils etc...
(I really would use my 4 wire milli/micro ohmmeter to check ground resistances to the star point, but not many people have one of those puppies..., so this should substitute)
http://en.wikipedia.org/wiki/Four-terminal_sensing
The volume pot is an acv-134, and is found in the sx-737, sx-838, sx-939 and sx-1010.
Thus until we find a donor unit, we're stalled.
It is a dual 250k ohm pot with ("flying") loudness taps.
Is the rotation smooth? or are there intentional "steps" in it's rotation?
It would be a real disappointment to go through all the trouble of finding and replacing the pot, only to confirm that the problem still exists.
Thanks for the BOM list. I will order at some point to eventually recap tone board. Bypass for now until I can fix the buzz issue. Sooner if buzz appears to originate there.
Volume pot is used part from a 1010, tested good by someone I believe knows these systems. Hopefully it helps.