usually, when people are using foam, they cut out sections of the wood, in your case it would be the centering rings, and then they lay them flat and fill them with expanding foam. then they cut them off with some hot wire, then they wet out some CF and lay it over. this makes for a lot lighter piece of hardware. you might have trouble keeping those centering rings flat when you lay over the CF and flatten it so there are no crinkles or bubbles. also, its a good idea to put the whole thing in a vaccum bag, but if you dont have access then you can just lay something flat over it. i find that fiberglass is easier to work with. and also easier to finish(primer, paint...etc..)
actually, the foamboard you're talking about, is it what i just described? or is it 100% foam in a solid state? because if you do decide to wrap foam in CF with no wood, i'd like to see the proceedure and definately a launch report. will you be documenting your steps?