How do I add links to the list of Special Sections in the Broadsheet footer?

In the Broadsheet footer is a menu that lists Special Publications. There's a max of 12 items per month (a bit weird, yes) and they're organized by publish date and must have attachments. This menu is managed via WordPress category, a special category called "Special Publications" (slug: "special-publications"). To manage this area, add or remove items from this category or manipulate their publish date.