Constrained layer damping means putting a semi-viscous layer between them, not rigidly gluing. I've done it with RTV silicone and had it work out ok. The squishy middle layer will work as 2 interfaces to absorb/reflect sound coming out of the box and will exchange vibrational energy to heat for low frequencies where the whole panel is moving. The tough part is you have to join the outer layer so that it can move without leaving obvious gaps in the box.
Ray
Aha! Viscous glue. Does RTV come in a tube like caulk? I haven't used it as far as I know.
Yes, the joinery could get interesting. OTOH it can be done with other wood furniture, so why not speakers.