I recently built a large event display and to add rigidity to the foam design I add a plaster to the outside. But this plaster is like cement when cured. It is hard as a rock and you can hardly grind it with an angle grinder. It used a powder as the base but there is a hardener that is added, very similar to Elmer's glue or modpodge.
I wonder if that would work and give you a fine enough finish. It could be smoothed out to almost glass like finish