I hope you will find this related to your problem somehow , I just finished building 4 channels of a high power Ab class amp, powered from a rather crude smps.I have a thread here on EE forums about the smps transformer core running hot, but that's another story.The thing that amazed me the most is that at first when powering only the first two channels I got some smps high frequency harmonics and noise through to the speakers, I almost made peace with that as I understood it's a crude self made thing and most importantly the noise was coming through the DC output wires as a sort of ripple leftover from the square switching waveform.
My wires , the ones coming from the psu to the boards etc are a rather big mess with wires going everywhere.
What i did is I simply sat down and thought what can I do , and I rerouted the input signal grounds and added some filtering resistors and guess what I hear no more noise in my output.
I'm not saying it's a perfect design now , no for heaven's sake , but I just proved myself that even with some messy wiring and far from low noise psu I can get decent sound simply listening to some advice and doing a bit of soldering the right wires in the right places.
So i guess it's not how the wires run in general but from where to where they run that's most important.\
I think the posters above are right the best you can do with heater wires is twist them locate them away from signal wires and let them be.Most of the hum comes from the filament itself and ground loops , I have had a fairs share of headache with ground hum.
As for the tube amps signal ground to chassis problem , well not always , I have two tube amps both have a metal chasis with tubes located inside and for both the signal ground is added to the chassis with the ground running also in the signal wire itself as the screen.at first I got a bit of HUm when I got the amps and I thought who puts ground like that but then I changed the old tubes and most importantly the filter caps, adjusted idle currents and output tube balance and now I'm silent.
Grounding chassis is not always a problem , it just matters how it's done.Those amps are from older times and they don't have the earthing third wire for the chassis , but I can touch the chassis or flip the power socket and nothing changes.Maybe a stupid advice but when your amp is running, maybe try to tap it with your fist a little to make the filaments shake and listen whether the hum gets louder ?
I did this with my older tubes and they got louder for a moment , with newer ones this effect is much less noticeable.P.S. why you say 120hz hum ? why would you get 120hz in a heater wire which is coming out of a 60 hz mains transformer?