@seamonkey where could I buy marine foam?[/QUOTE]
The structural foam as used in marine applications (also aerospace, Motorsport etc) is a lot more expensive than styrene foam . You wouldn't want to use it without a carefully thought out structure. If anything it would be less effective than your styrofoam used on its own.
This is an example of the stuff... Link Removed
It would be interesting to try something - the potential is there for a moderately light, but very high stiffness and also very expensive cabinet. It would fascinate me to AB a sandwich construction cab against an internally identical birch ply one, but I just don't have the facilities for sufficiently sophisticated testing, nor probably quite the energy.