As for the Azog stuff, wasn't it Dain that takes out the Goblin king's grandson (or something like that?).
As for the White Council, that makes sense, but if he's still looking for where Isildur lost the Ring, and wants it for himself, wouldn't Gandalf and the rest of the White Council, looking for the Necromancer, buy him more time to keep looking? I don't see why acknowledging that evil has returned and that they should check it out, would keep him from searching for the ring.