I haven't heard of anyone previously having exactly this problem, so I don't know of a definite solution.
However, in your place, I think I would be trying two approaches. I would contact the CO, saying you know s/he isn't responsible for your case now it is finished, but can s/he please tell you who to approach to "unstick" this problem. I would also phone the call centre again. The telephone answerers won't be able to tell you anything useful, because they only work from a database, but you can ask to be put through to a supervisor or other case-working official, to ask the same thing - who can you take your problem to, who can cut through the red tape here? The bottom line of this is that INZ already HAS your passport, just in the wrong office, and it's surely not beyond hope that the two branches could liaise with one another to sort it out, whereas you, as a member of the public, haven't been able to access anyone to pull the right strings.