Modifying the django_session table to add an explicit user_id can make life a lot easier. Assuming you do that (or something similar), here are four approaches to munging things to your liking:
Fork the djago.contrib.session code. I know, I know, that's a horrible thing to suggest. But it's only 500 lines including all backends and minus the tests. It's pretty straightforward to hack. This is the best route only if you are going to do some serious rearranging of things.
If you don't want to fork, you could try connecting to the Session.post_save signal and munge there.
Or you could MonkeyPatch contrib.session.models.Session.save(). Just wrap the existing method (or create a new one), breakout/synthesize whatever values you need, store them in your new fields, and then super(Session, self).save().
Yet another way of doing this is to put in 2 (yes, two) middleware classes -- one before and one after SessionMiddleware in your settings.py file. This is because of the way middleware is processed. The one listed after SessionMiddleware will get, on the inbound request, a request with the session already attached to it. The one listed before can do any processing on the response and/or change/resave the session.
We used a variation on this last technique to create pseudo-sessions for search engine spiders to give them special access to material that is normally member-only. We also detect inbound links where the REFERER field is from the associated search engine and we give the user full access to that one article.