Maybe you could use 1" styrofoam insulation instead. You might have to
reinforce it at certain mounting points with epoxy, but the result
should be as light as polystyrene. Also, you could find a plastics
supplier that would have almost anything. I have one locally named AINS
plastic. They could ship it I bet. They can cut to any desired shape
too, given your pattern.
It sounds like a fun project.