...you just deleted them (R4, R7) from the circuit and this stopped hum?
Yea.
Well, I can't understand that. Either the transformer works in very tight conditions and additional, even small, load drops voltage to the level that is not appropriate for LM regulators or the resistors are wrong valued and draw excessive current. It cannot be the source for any loops really. I'm not guarding the resistors (while understand their job), but such effect...
if the case isn't connected via a .1uf and 150ohm resistor to the ground on Bugle then there is hum
It is not surprise for me. You said the Bugle is the only place where the whole chain is grounded. Eliminating this only point sure will have effect.
Actually the effects of RF ferrites on the power cord have been effective like a stereo upgrade.
RF ferrites is just simple hi-freq common filter. You said you already have one in the device, or I'm wrong?