I have been trying to get the quest to fetch Roggi's ancestral shield so I can have him as a follower, but the only dialogue option I get is the "How do you know so much about mead?" line. I have tried doing the misc quest to clear his bar tab, but that doesn't help either.

How do I receive that quest?

Make sure you don't have any other radiant "retrieve item X from location Y" quest ready, I think the game only allows one radiant quest of a given kind to be active. If you do, complete it and try approaching Roggi again.