Maybe a piece of https://duckduckgo.com/q=thermal+interface+pad https://duckduckgo.com/q=thermal+interface+pad could do instead? They come in various thickness.

Maybe a piece of https://duckduckgo.com/q=thermal+interface+pad https://duckduckgo.com/q=thermal+interface+pad could do instead? They come in various thickness. Depending on where the coils are located, and if they are in some sort of airstream or not, I'd try that. But only in one piece, not several layered above each other. Could result in dampening the whine, or eliminating it altogether, and better cooling. By pressing on the coil on one side, and some part of the inner casing on the other.