think of it the same way as the stringers, they are there to help strengthen and stiffin the hull bottom. same thing can be done for the deck. though glassing them in will be a pain. very messy especially if you plan on doing it without turning the boat over. maybe you can wait till you do the bottom.
the foam may work, but i would think to make it stiff enough you will need alot of it and thats tricky to not put too much. it can expand too far and ruin the deck.
OldRigger would definatly be a good guy to talk to about that. unfortunatly he will be away for the rest of the weekend. im sure he will be happy to help ya.
by the way, the boat looks nice. id put a few bucks in it. but then again, im not the sharpest tool in the shed.