I was able to end the staff quest but I did encounter two different bugs within it.
Bug 1. While fighting the fire elemental, I used a scroll on the first round to summon an air elemental. I ordered the air elemental to immediately attack the fire elemental. My air elemental missed, and immediately took -2 feedback damage as if he had hit the fire elemental... he took that -2 feedback damage over and over and over again in quick succession until he died. I don't know if this particular bug is specific to the staff quest, but it is where I encountered it.
Bug2. After completing the staff quest, I was joined by the fire mage champion. He looks pretty cool and all, but he does not appear to register as a champion, just a unit. I cannot shop for him, trade items with him, or in any way interact with him as if he were a champion. I ended the turn once in the hopes that he would turn into a champion afterwards, but that did not occur.