Having read all the posts so far, to my mind, post #4 seems highly relevant
From that - and what you have said, quote: hum is much worse if I am near the set, but if I move away by at least 5 metres then the hum becomes barely audible, unquote, leads me to wonder if it may be that the mains wiring radiation is being picked up by your body and re-radiated. Yes, really weird, I do appreciate - but you do seem to have a
very strange fault condition.
However, this may be of assistance:
https://www.vintage-radio.net/forum/...ad.php?t=42507
If it isn't radiation from the mains, then it must be that where you are located there is a strong radiated electro-magnetic field that could be coming from a nearby radio transmitter - or some other source. Perhaps it's coming from a high-voltage street step-down transformer: it's entering your body and re-radiating.
Perhaps, with the aid of a portable transistor radio that shows same problem, a travel around your vicinity - which might be a few miles - might locate said transmission source.
I'll be intrigued to discover the cause - as I expect you will be - and other member here also!
Al.