I retract my lacquering suggestion. Google shows I have no clue.
Apparently, the winding that may be vibrating could be internal/deep, so lacquering the top might not do anything. Also, the solvents in the lacquer might dissolve the insulation on the wires, lol. Shims are apparently the thing to do. Small bits of mylar or whatever you can wedge between windings without damaging it. Probing with a stick to find the right spot might help? Careful with mains, of course. Seems to me that tightly wrapping over top the windings with plastic wrap or even just STRING might get some pressure into the right spot, too? Maybe with a small bit of something underneath to get more pressure on the actual windings, not on the core/laminations.
Also, if the filter cap is bad, it could be increasing the problem. Replacing the can might be worth a shot.
Might be worth a shot to see if the seller will view your video. And see if you can do an EXCHANGE, if you BUY a second station and return the first one in the new packaging? The seller doesn't risk losing a sale and/or getting a product he can't resell. And you get a second chance, at least, lol. (Maybe if you sent the same station to someone in another part of the grid, the thing would be dead silent?)