Constrained layer damping tape on toroidal transformer?

Uh, the transformer is not “live”.

Siri, how does electromagnetic energy transfer work ...

Geez, you’re still trying to argue that? Get real! 

If you're going to use damping tape, try the best - fo.Q TA-102 piezoelectric damping tape. No, I don't make it or sell it (or anything else). But I buy a lot of it for my own use. In fact, I'm probably a bit obsessed with it. Goes way beyond normal mechanical damping, the embedded piezo particles convert vibrations to electrical current, and then to heat which is then dissipated into the tape compound. Many other damping materials only operate on a narrow-ish frequency spectrum, leaving muddy frequencies to bounce around. Many other materials are optimized for high amplitude vibrations, whereas fo.Q is most effective on very low amplitudes such as the vibrations found in audio components. It's slightly conductive.

My solution is multi pronged. Remove bolts or at lease loosen them. The only purpose for the bolts as far as I can see is to hold the transformer when the component is shipped.  Place the transformer on pure natural cork square, thickness 0.25”

Next, remove almost all screws holding the printed circuit boards to the chassis, at a minimum loosen them. Use small pure natural cork squares to shim the printed circuit boards, isolating the PCBs further from the transformer.

Next, use 3” or 4” lengths of pure natural cork 1/8” thickness to weave like a serpentine wall around and through stacks of capacitors to reduce their vibration.

Finally, wrap the large transformer with two (count em!) thicknesses of mu metal to shield everything in the component from the very toxic magnetic field generated by the transformer. One thickness of mu metal is 75% effective. Two thicknesses of mu metal separated by 1/4” is 92% effective.

As Bob Dylan says at the end of all his songs, good luck.

@geoffkait - YUP!

You can purchase mu metal on eBay.
You can purchase dampening material already recommended above or go to the Mad Scientist website and buy his reese's pieces things and place them on the transformer with good results.
You can buy transformer covers.
You can buy copper plates and isolate the transformer using double sided tape to hold them in place if you can.
You can buy a separate aluminum box on eBay and move the transformer out of the one chassis.

Happy Listening.