Did this via HK in 2017 (coming back via SYD although I booked AKL-SYD separately in Y on Emirates) )on Cathay. It was <2000pp, found using google flights alerts about 6 months out.

One option would be to use the 2-4-1 to KL/SIN or other SEAsian and benefit from a stopover - it’s a long long haul. I think if it’s the BA reward flight to SYD you can’t atop en route (but that may be incorrect!).

From Asia there are lots of options on the NZL routes (and you also have other options like Wellington and Christchurch.).