I recently found out that there's a stone pot that functions like a barrel. Is there, similarly, a stone substitute for bins? Or any other material that isn't wood or metal?
And don't forget, you can also store almost anything in mine-carts! They are normally made out of metal, but you can also make them of wood. They haul/hold more than any other container in the game (8.3 times as a barrel or large pot, and 5 times as much as a wheelbarrow), and your dwarves are not slowed when pushing them, unlike the weight movement penalties they have when carrying containers or objects.