Aha. Someone who actually knows something has stepped forward!
So if your transformer output cannot be lowered from 16V AC to 14V AC, try additional diodes as shown. 3 additional diodes on each side as shown lowers the effective AC voltage from 16 to about 14. You can add more diodes if the hum is still objectionable. Presumably you bought/have more than 2 diodes since you usually have to buy a pack of 10 or whatever! Or 2 cents a piece - free shipping from Asia.