... a hum from the power supply unit itself, not through the speakers. ...
Doc B's suggestion of Roger is worthwhile - Roger is extremely capable. If there is a circuit problem causing this, he will be able to find it and fix it.
Assuming no circuit problem, the noise seems most likely to be a power transformer vibration. There are two approaches - replace the transformer with a more robust unit, or work on silencing the unit you have.
If you have a part number (it may be a Hammond?) I can comment a little more on options. A photo might show whether there's room for a larger transformer.
Otherwise, tighten the screws holding the transformer together, if they are loose - they don't have to be super-tight, but loose is a problem. Tighten the mounting screws. If the transformer is not isolated (a photo would help here, too) there may be some other useful things to do.
My two cents.