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.