I work in the auto damage industry and I've been picking up large sheets of foam for free from body shops. New plastic bumpers are delivered in the foam. Some of the foam is reused for the same purpose but much of it is discarded. These sheets are thin but large some up to 5'x12' I've been using them in my trailer to cushion gear but have also considered lining my dry box.
I would bet many shops would make an exchange.