Thank you for the helpful comments, folks. I sealed the hole at the bottom of the chimney, and that seems to have caused a noticeable increase in the draft. We've tried burning it hot today, and haven't had any trouble with smokeback yet. Maybe that will be all we needed to do!
I don't know how to tell whether the
superwool is forming a good enough seal in the gap where the doors used to be. I'll try holding a lit match near it to see if there's any air movement toward the seal.
I haven't tried raising the plunger tube yet; as I said above, maybe I won't have to.