ASC (Acoustic Science Corp.) offers a product named Wall Damp. It comes in 4" squares (I believe) and long strips, and was designed to act as constrained layer damping when installed between layers of sheetrock. I recently heard it's effectiveness (in Audiogon member folkfreak's music room), which is fantastic! Art Noxon states that the huge 4' x 8' sheets of drywall, when confronted with sound waves and other vibrations, behave as do drumheads when struck---bend, bow, and flex, creating an audible resonance. Rap your walls with your knuckles---they make a clearly audible sound, not a good thing. Folkfreak's walls sounded like slate when I rapped them! Wall resonance is a commonly-overlooked characteristic of the acoustic behavior of listening rooms imo---the final frontier!
ASC sells the scraps and end pieces from Wall Damp installations by the lb., for real cheap. I just bought a lb., plenty for putting between 1- the two pieces of acrylic (or one of acrylic, one of aluminum; I haven't yet decided) that make up the pickup-arm mounting board of my newly-acquired turntable, and 2- the two 3/4" layers of my table's shelf. I will bolt or screw the two together, with a layer of Wall Damp between them. Sounds promising, ay? I can't see a downside, in theory at least.