I like the ingenuity but I think it's kind of a waste of expensive material. CF is very stiff for its weight, but steel is equally stiff. Since the weight isn't much issue, use steel. Want damping, then use steel box section with foam or sand inside. For sheets of aluminium or steel use constrained layers (I mentioned green glu before, bitumen and butyl rubber sheet is also good).

I design loudspeakers and in this area we pay a lot of attention to damping sheet materials for the speaker boxes. The BBC did a great amount research on this and concluded that constrained layer damping was most effective, although making it stiff was not the goal. So IMO use stiff materials and constrained layers, but don't worry much about weight.