Basically the only realistic inventory on NZ as Lack has said above is PVG - AKL. Until November you might have some luck, but forget about the Xmas period.

Mucking about in the Aeroplan award finder I see PVG - SIN - MEL - AKL - ICN - PVG in J. With a stopover in MEL and a destination in AKL you could easily see both countries in one go.

Do your research and call the M&M phone service only when you know exactly what you want.