Check the ground braid is connected to the shell of the speaker. (yes)
Check the ground braid is connected from the base cabinet to the headbox. (yes)
Move the two POTS on the sound board. If this solves the problem, or makes it worse, you need to clean the connector pins, replace the header pins or reheat connector pins and POT legs on the Sound Board. (No difference better or worse)

Check the voltage at the solenoid driver for the displays is no more than 185VDC. Could be a bad Ground connection in that circuit. If you have another Bally, you could try swapping this out. (not checked).

Still having problems ?

Game OFF

Remove all displays except Player 1. Switch on game. Still noise ?
With the game OFF, add a display, each time testing to hear WHEN the speaker starts to HUM when you switch on. This would indicate a bad ground on one of the displays. I've only ever seen this once. (Once I took off all the plugs, the noise dropped considerably). Put them back on and although the noise increased, it is still 20% of what it was. Thanks very much Nino.