Well, I think the transformers are either mismanufactured or poorly designed. When you design a transformer you make a deal with the devil. If you use lots of turns the transformer will be quiet, but the large number of turns means smaller longer wire which causes higher resistance so the transformer becomes less powerful. Or, you can make the transformer bigger without increasing the power, that costs more money.
If in fact the transformer is humming because it doesn't have enough turns on the primary, then the only thing one can do that I know of is to lower the voltage to the amp. This could be verifided by using a variac to lower the voltage and see if the hum goes away. More diodes will lower the voltage some. Or a stepdown transformer that dropped the voltage from say 120 to 110 votlts. Of course the step down transformer might hum. I presume you have two diodes in parallel connected anode to cathode. Each time you add one of these it will drop the line voltage about .6 volts. It also increases the lines harmonic distortion but that shouldn't be a problem.
If the hum is being transmitted into the chassis you might reduce hum by placing the amps on something soft. If there is a cover that is vibrating you could try removing it.