How would you damp the hum from this transformer?

After a second dunk, I now have a nice quiet transformer with barely audible hum. Now the hard part: when I put it back in its box, the hum becomes a lot louder. I need to figure out a good way to assemble the box without it resonating - using some rubberised foam to damp the vibrations doesn't seem to work. The thing that makes it hard is that the transformer was housed in a folded metal box, apparently stuck together with varnish. I guess trying to stick it back together in the same way is the way to go...
 
I have a Sony TAN-15F amplifier, which sounds beautiful, but is rendered unusable by a transformer that hums loudly enough to be very irritating when music is not playing. The seller told me that it was quiet before it was shipped to me, so I decided to take this as an opportunity to learn something about transformers. How hard can it be, right? ;)

So far I've managed to open the metal housing of the transformer, which was a pain as it was a folded metal box coated in lacquer - and held together by the lacquer, too.
The grey metal band wrapped around the core appears to be stuck in place with yet more lacquer, which limits my options for further disassembly.

I have identified that, if I squeeze hard all the way across the left and right sides of the sheet metal band that crosses over the copper strip, I can considerably reduce the hum to a level that should mean it wouldn't be audible (or at least not irritatingly so) after boxing back up.

Since this transformer isn't of traditional construction (see the pictures) I don't have an option to just "tighten everything up" in the normal way. There is a gap between the grey metal band and the copper loop - if a suitable approach would be to pack that with something, what's a suitable material? Or does anyone have other ideas for possible solutions?
Does the shielding band have its own connecting lead, separated and electrically isolated from all other leads as well as the case?
 
I did say:
"Any thick slightly soft material will do."

Alternately, rubber sheets, softer than tread rubber, bitumen washers, silicon caulk, whatever is handy.
For me, gasket paper is handy, and in fact here too asbestos roofing sheets are out of production.
Did not check the composition for gasket paper. Used to have asbestos, 20 years back.
3 mm thick, we cut with a chisel, no power tools or powder flying about. Draw shape with marker, chisel is an old HSS tap, and a 1 kilo hammer.
Simple...
1644864591755.png

Water gasket sheet sample.
This is what I have handy, locally made Champion brand, or similar.
 
Stick the shield back on the transformer, and as for foam, the transformer can get hot, so use automotive grade heat resistant material.Or alternates, as described above.

Shield is more for EMI shielding than noise absorber, check for continuity with chassis after fitting.
And check if the unit has an Earth connection, if yes, then transformer shield to Earth must be continuous.

Could be the transformer is having resonance with the body.
Also, if you took pictures, put it back in the same orientation.
If the noise is mild, leave it alone, the varnish will fill the gaps in a few warm cold cycles.

Enjoy the music.