What I did was to keep the assignments in a read-only category and had students create their work as topics in a category reserved for that section of the course. That allows students to come back to the course in the future to see their work and doesn’t require any deletion or moving of topics for new sections.
If you really want badly to drip-feed the stuff, you could have a plugin that added students to the next-week’s category on a schedule. I’d guess that $500-1000 in marketplace would do that, depending on how much customization was possible in the plugin code vs the admin interface.