I ended up calling NZTA, the person on the phone seemed to know what I needed.
10 minutes later I had an email from NZTA with a "Letter of Entitlement". I printed this and sent it off with my application. This was sufficient to get my license transferred with manual endorsements.
It would seem, that since the Immigration Act 2009, this is no longer possible without an NZ Citizen Endorsement in your other passport.
Since the application may take up to 31 days, contacting the Immigration New Zealand asking how to deal with this matter under emergency circumstances such as yours is advised.
If you are a New Zealand citizen but ...