Is it feasible to decouple the internal hard drive cage (holds 5 or 6 disks) from the
case frame, perhaps by some highly-compliant isolating bushings?
I have a Lian-Li PC-6085A. I've actualyl decoupled my Seagate Barracuda IV using elastic inside the drive cage. The drive isn't mounted to the cage directly.
You probably can mount the drives in the cage normally, and set the cage on a isolating pad of rubber or foam on top of the normal mounting point. I don't recall off hand how much space I have in my case between the cage and the drives, but I can check if you want.
The way my drive cage is installed into the system, is by a tab on the cage that fits into a slot on the case on one side. And, a pair of thumb screws on the other side hold the cage down securely. You can put rubber grommets between the thumbscrews and the case, but I don't think there's enough space to do anything on the tab/slot connection.