Thanks to a tip from Bill Fitzgerald, I checked out a copy of the Leech module for Drupal. Despite the rather bad name, it sounds like it is (or eventually will be) perfect for what I need.
It lets users add their own feeds, and can associate said feeds and subsequently aggregated items wit any of the user's Organic Groups. That takes care of the Class/Cohort/etc... concepts. Users just create or join the appropriate Organic Groups within the Drupal site, and add whatever feeds they want to whatever Organic Groups they want. They could add subfeeds of a blog to different OGs (say myfancyblog.com/tags/bio680/feed to the Biology 680 OG, and myfancyblog.com/tags/poli544 to the Political Science 544 OG...)
It's not firing on all cylinders at the moment - I think it's failing to add items to the specified OG, and some other minor things. But it's going to be waaaaaay simpler to just roll up my sleeves and help out on Leech.module than to write anything from scratch.
Combined with stuff like the Views module, this could be an insanely powerful tool to help pull disparate feeds for users, spread across the internets, into a cohesive community site that behaves organically depending on the whims of the users. Very cool.