Pavel, thanks. I took the lid off and tried to discern where the noise is coming from. Poking around with my finger I couldn't detect any vibrations on or near the transformer (it's a large R-core type, maybe these are more prone to vibrations) or large capacitors. Listening closely it was hard to say if the noise was actually coming from one part of the amp or another - I imagine whatever it is is being amplified by the casework. Lifting the unit at the front also reduces the hum, so there's definitely some interplay there.
If it's indeed the transformer, you could try tightening the screws that are holding it to the chassis. Also adding something pliable (like pieces of an old mousepad) between the chassis and the cover might reduce the audibility of vibrations.
Would that be a zobel network? Until now I never had any major problems with interference on my chipamps in over 20 years (unless a nearby mobile phone starts ringing of course!) so always felt it best to leave such things off. I could be tempted to build a small external 'dongle' to add before the amp if that would work...
No, Zobel should be used on the output to isolate the amplifier from capacitive loading and ensure its stability. I am talking about an RC low-pass filter at the input. This, for example, is from a line level preamplifier that I have designed recently:

C101 is a DC blocking capacitor, but R102 and C102 form a low-pass filter for RFI suppression. Pay no attention to the diodes, they are included merely to protect the opamp in case voltage at the input exceeds the supply voltages.