Had a similar experience with a JBOD chassis. The vibrations of the spinning drives caused resonance on some positions. The cure was to attach a patch of duct tape with a washer at a certain point on the chassis.

This is a classic: https://www.youtube.com/watch?v=tDacjrSCeq4

And a evolution of that https://www.youtube.com/watch?v=ntw32kYDryM

Heh I remember in the late 90s I put some rubber between the hdds and case to greatly reduce the noise of my desktop PC.

My previous PC had the option of inserting harddisks in rubber bands instead of screwing them to the frame. It was a case specifically aimed at noise reduction (the Antec Solo).

I have seen rubber 'sleeves' for hdds

I don't understand why this isn't a standard practice.

That sounds like a really easy way to make a hard drive overheat.

Way back, I had a 4GB SCSI hard drive that was extra tall, extra fast, extra noisy, and extra hot. I constructed a thick rubber box around it to try noise-proof it a little, but I also had to strap a CPU cooler to it and have the airflow enter the box and exit at a hole in the box after wrapping all the way round the hard drive. It worked. But just wrapping it in rubber would have been a very quick way to cook the drive. This is a drive that if just left running bare on a table would get too hot to touch.

Hard drives produce a heck of a lot less heat these days.

An elastic mount does not have to be a suffocating box.

Plus, and I could be wrong here - the mounts are not really designed to be heat conductors (the rails are plastic on my high end Dell workstation); I suppose the heat is extracted via air flow.