I have a 10w diode laser, and have successfully built foamboard planes with it on my CNC machine. It doesn't cut all the way through the foam board, but it does easily cut the paper backing. If you etch the paper on both sides of the foam, it is easy to follow the score lines with a knife to cut it out, or break the foam along the straight lines. You just have to prepare a mirror image of the top-side pattern to cut on the back side of your material, and place some reference marks on the mirror line for maintaining alignment. You don't need 10W to cut the paper, so I am sure that a lower power laser could do this also.