If grounding the middle lug of the normal volume pot reduces the hum, that indicates a problem with the normal channel preamp. Check all the solder joints on the grounds of the input jacks and the grounds on the circuit board. Could be one of them was questionable and now has worked itself loose. There is a chance V1 has gone bad, too. If you have another 12AX7, or any tube in the 12A_7 family, you can try changing V1 and see if that makes any difference.
A shielded cable running under the board wouldn't be quieter than one running over the board. Anyway, it wouldn't suddenly start causing hum in an amp that has been working well. As long as the shield is connected to ground at only one end and it's insulated from ground at the other end.
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