Perhaps someone who has a Lian-Li case (or who has looked closely at the inside of one)
can answer this:

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?

From photos at Newegg, it appears that in the Lian-Li mid-towers, there may not be
enough clearance between the top of the hard drive cage and the bottom of the floppy cage.
Moreover, there may be clearance issues where the drive cage attaches to the case bottom.

Anyone know?

This question is of particular interest now that the noise-reduced Lian-Li PC-6070 is nearing availability.

There's less than half a centimeter between the drive cage (front bottom) and the "regular" 3.5" cage (mid bottom)..

i have been thinking somewhat similarly, instead of decoupling the hdd:s in a 5.25 slot and have a lot of unused 3.5 slots, couldn't you decouple the entire 3.5 drive cage, the bonus could be a decoupled floppy drive and maybe you wouldn't have to use sidesinks since the drives are still mounted in the steel drive cage.

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.