Some (most?) HDD have underside mounting screw holes. Using those, and a rubber grommet, you can prevent the HDD from transmitting its vibration to the rest of the case.
But your problem is different.
With a high pitched noise, you want to encase your HDD with something solid, preferably a metal. Of course it won't be very practical, because it still needs to vent, so I'd recommend a "muffler" approach, where you encase the HDD on four sides only, in a steel cage, as is found in a lot of cases nowadays.
If you have some extra steel (like from the 5 1/4 bay covers), you can suspend them on the remaining two sides.
You'll have to experiment, but that's your basic guideline: high pitched noise is blocked by a dense object. A low pitch noise is blocked by a low density object.
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