You can use the Amex and GUF together, to get yourself from CW to First, and use the Joker (if necessary) once only to force availability.

I go from NCL to NZ twice a year, for relatively short stays, have been doing so since I was 12 years old. Over that time I've come to the view that the most comfortable and enjoyable way to do it is to go via HKG (if paying) or KUL (if on points/Avios). And stopping over for a night or two or three. Going direct misses so many great places en route, and I've never taken a shine to SIN, and one misses the old BKK service.

Now admittedly I'm going on to the South Island, so further still than Auckland, but have a look at the KUL options now that BA are back on the route, and if you haven't been to HKG, now is the time.