I agree with Finski and Robo, based on my experience with the all season inner cover, they do eat the polystyrene pretty quickly.
BUT, Acebird's experience with urethane glues makes me believe one could adjust the dimensions out a 1/4 inch each direction and laminate some 1/8 inch luan to the intertior, so the bees won't chew the polystyrene.
@Robo,
Have you ever split full hives in the fall and placed them in your nucs and added a queen? Thx.