I magnetized all of my walls and found that metal mesh paper organizers work perfectly. There is enough steel in the mesh that the walls will hold to them. Also depending on the organizer, you can get one where the shelves slide out so you can simple pull a shelf out that has all the walls magnitized to it and bring it right to the table.
Not sure I can post the link but I bought 3 of these off Amazon for $20 each
"Veesun Paper Letter Tray Organizer, Mesh Desk File Organizer with 3 Tier Shelf Sorter with Drawer,Black"
They fit perfectly in a Kallax (Ikea) square and 90% of the walls fit on a shelf. Only a few of the tall walls don't and they sit on the top of the organizer. Any of the overlays fit perfectly in the drawer at the bottom.