Help! Cure for transformer hum?

I've had a 1987 vintage NAD 7600 Monitor Series receiver that I've loved for 30+ years. It finally began to show various signs of age and, at just that moment, another that had been stored for most of its life, in the original packaging no less, came available on eBay. It wasn't cheap, but it seemed to be in "like new" condition, so I bought it. 

Well, it's pretty all right, "like new" in appearance, all the circuits work as they should, even the pots are quiet--but the transformer makes a 60 Hz mechanical hum. As I understand it, transformers contain plates that are stabilized with glue which becomes brittle over time and can crack or loosen. In any case, my old, semi-functional but otherwise identical unit, didn't hum. So, after consulting various knowledgable friends, I contacted an authorized NAD service dealer about 200 miles away, took both units to him, and he swapped out the "old" transformer for the "new" one. 

Maybe it was the 400 mile round trip in the car that caused some kind of break in the old, brittle glue bonds of the previously silent transformer, but installed in the "new" 7600, the unit still hums; not as loud as before, but we audiophiles are perfectionists, and it bugs me. It is, fortunately, a mechanical hum, as I mentioned, so I don't hear it in the speakers--although it does get picked up by the tuner.

Is there anything I can do to solve this problem? The transformer is securely mounted to the chassis, and I've tried putting additional damping materials under the feet of the unit. No improvement. I've tried different wall plugs, both with and without a power conditioner. No improvement. 

Of course, it seems likely that the only solution is to replace the transformer with one that doesn't hum. But where would I be able to find that? And is it even worth doing, given what I was told about the time-degraded glue that keeps new transformers quiet?

The repair guy told me (and showed me) higher-cost transformers that are entirely encased in metal; those will never develop a hum, he says. Is it possible to encase one of these original transformers in some way in order to silence it? If so, who can do that?

Sorry for this probably futile plea. Obviously, one solution is to eat the $1,000 I've already spent on the "new" unit and just buy something else that's really new. But I don't want more than two-channel stereo, I don't stream, there are various smart features of the NAD that I would not want to sacrifice--and, best of all, it sounds great in every way except for this damn hum! I've had the option to replace it with a couple of different, and presumably better, devices, most recently a Primare A30.1 integrated amp, which a friend owns and is willing to sell. I had the Primare in my listening room for a month, and liked the sound of the NAD better. Plus, of course, it has a great phono circuit, a tuner, very useful semi-parametric tone controls, a powered balance control, and several other wonderful features. 

Thanks for any advice you can give me.
I had power conditioner and tube amp transformer vibration or hum years ago, did the back to back caps on AC line, helped. Ultimately, I discovered it was over voltage from power company causing hum, 124-126V was typical. Ever since then I monitor voltage 24/7, has stayed 119-121v for well over three years, no transformer hum since, no longer have the caps on AC line.
Some updates on this issue, for those who may be interested.

First, I tried a DC blocker (the iFi unit). No effect. Frankly, I had thought this was a long shot; after all, the unit didn't formerly make any noise--it had been dead quiet for 30+ years--and no other transformers on my home's power, audio or otherwise, make any noise.

The "dip and bake" suggestion seems to me to be the best proposal, short of just living with the noise or replacing my beloved old NAD unit with something newer. However, I'm not sure I want to mess with heating varnish in my kitchen's oven, for the obvious reasons. Chris_w_uk is the Audiogoner who described this process, identified the varnish I would need to use, and then even provided me with a link to a company that may be able to do this for me (at his suggestion, I tried to locate such a company in my area, but none of the likely candidates really understood what I needed). So I've emailed the company Chris sent me the link to, and I'm still waiting on their reply. But I want to thank Chris for his well-informed help.

Re-capping has also been suggested, and I know this is something I probably ought to do for lots of other reasons as well. But my intuition tells me it is not likely to resolve this particular problem. I won't go into my reasoning here, but if any of you think I'm wrong about this, let me know.

Finally...the "noise" is, after all, very subtle. I can't hear it at all while I'm listening to music (except between tracks), it does not seem to affect the SQ in any other way, and even with the room completely silent, the transformer hum is faint. My home's deluxe HVAC system is louder, and so is the refrigerator two rooms away in the kitchen. I have an audiophile friend with a designated listening room full of far more expensive equipment than mine, and he doesn't seem to be bothered by an ambient hum from some household device in the vicinity that is much louder than my transformer hum. So, really, this problem is more psychological than musical. And yet...we audiophiles are perfectionists. I can tolerate a noise in a fridge (although I chose one based on how quiet it was); I can tolerate wind noise in the trees outside, or birds, or the occasional plane overhead. These are not flaws in my audio system, unless the term "system" is construed broadly to include everything in the audio environment, including one's own ears (and who among us has perfect hearing, or doesn't suffer from minor tinnitus?). Be all that as it may, I am insanely intolerant of any perceived flaw in my audio equipment itself. So perhaps this "problem" is really mental. Maybe I should learn a lesson from it.

Thanks for everyone's contributions to this thread.
I have posted this before... Hum is very rarely caused by DC on the line. I have a PS Audio Humbuster, still NIB which did nothing in my case.I actually had 2 causes:  In my tube preamp one of the toroidal transformers needed to be rotated about its axis to minimize hum, my repair tech did this while I was on the phone with him. My other cause was 20 year old filter capacitors in my  SS amp. I replaced those myself, and all hum was gone. Please don't burn your house down by putting varnish in your oven.
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