Just offering an opinion here. I don't have any experience with polystyrene, but in the past few years I have gotten a lot of carbon fiber laminate part design and stress analysis. Carbon fiber is great if you can mold the structure as a single part and not put a single hole anywhere. The weakest part of the design with multiple parts is the bolted joints. You CAN NOT drive a screw into this material and expect it to hold very well.
From what little I know of surfboards, they have a foam core with polystyrene laminate over that core. This is very similar to honeycomb core parts I've dealt with. Very strong in bending, terrible in shear. With the torque box design most are utilizing, the walls, roof, and bulhead wall take considerable shear loads.
Now, all that being said....you could make this work. You have to design the outer shell (walls & roof) as one part. The bulkhead wall would have to be bolted in. Bolts....not screws. This is possible, but I wouldn't think it worthwhile. Of course this is the conservative engineer in me!
