Constrained layer damping works by having two materials of different acoustic impedance in intimate contact.Wood and elastomeric glue are quite different, but you may fare better by using one layer of wood and another layer of metal, joined by elastomeric glue: aluminum and lead are two of the best choices.
When I built my music room a few years ago, I looked at many of the elastomeric products, and found M1 from Chemlink to be a good all-round choice. They also have a product which has marginally better adhesion - but look at the specs of anything you use, because some of the stuff called 'glue' really isn't.
Good luck!