This may seem trivial, however I have been unable to find any practical way to listen for skill advancement other than with a story manager. Is there any way for a script to listen for character skill advances with no additional dependencies?

maybe http://www.creationkit.com/RegisterForTrackedStatsEvent_-_Form, but i've actually NO idea if that catches av's

(and since i assume it's your av-caching-thing you want to do with this, you'd have to register for LOTS of them)