Doesn't Saturn have three rings, two really faint ones? Some planets do at least. That would mean two are not directly above the equator, and would move across the sky as the planet rotates. Anyone who actually knows anything about this, feel free to correct me

Also, I don't think it'd be a problem if the ring collapses mid-story; some of the short stories would take place before the collapse, some during, and some after, or that's how I interpreted it anyway