If the objective is a NZ ATPL, do not be tempted to stop over in Aus and do the CASA ATPL then convert via the TTMRA. As mentioned, if the Aus licence is a conversion from another licence, there could be a problem with having the follow on conversion to NZ accepted.
With B737NG on your FAA ATP you should be able to do the test on a 737 classic simulator in NZ. It is all the same type rating. I believe the old Air NZ device is now owned by Air Chathams. Someone else should know its status.