Hi Chris, as a '57 owner I sympathise and am sorry to hear of your troubles.

I know these speakers inside out so am curious to know what causes the hum. You say the 'boards' were also changed, do you mean the high voltage (multiplier) boards?
If there is any leak on the panels then the high voltage is pulled down a bit due to the very high impedances involved.
When this happens you can get a small hum on the panel, noticeable when you put your ear to the speaker.

One of mine has this very slight hum, inaudible away from the speaker, but I know there is a slight leak. I fitted aftermarket high voltage boards that have a neon light in series with each panel. This flashes at very slow rate if there is leakage and flashes faster if the leak is greater, one of the lamps in my speakers flashes every 1.5 seconds.

If the speakers are perfect there should be NO hum.