You may have only four stopovers in Oceania (SWP) but you have five segments. Outside of your continent of origin (NA), it is segments that count, not stopovers. I suggest that you drop one of the NZ segments (AKL-CHC or CHC-ZQN) and buy a Qantas ticket locally, either a "Red e" deal between AKL-CHC or a regular economy ticket from CHC-ZQN. If you pick the right flight, it should cost you less than US$50. Much cheaper and easier than trying to add a segment to your OWE ticket. You can buy the ticket online at the Qantas web site.

Otherwise your itinerary looks OK.