Styro-foam is a registered trademark of Dow Chemical. The actual material is extruded #6 plastic polystyrene. And it can be recycled.
The problem is there is no money to be made in recycling this product so those recycling facilities that accept it are only doing it as a benefit to the environment. With a 1,000 life span it's going to be around awhile.
One alternative would be to require comp organizers to ship their used styrofoam to one of the recycling centers that accept this material through the mail. Maybe not the best solution, but it's a solution.
Another alternative would be to require them to spray the containers with Lemonine. This naturally made citrus product will shrink styrofoam to 1/20th of it's original size. This process would at least take up less space during the 1,000 years it sits in the landfill.
There is also a box of the same dimensions made out of sugar cane that biodegrades in 120 days when used.
Thank you, Yak for bringing this issue up.