There is sporadic space close-ish to departure. This is a relatively new development after ANZ had pretty much zeroed out award space for years.
Back in March when I was considering a trip to NZ in April, I was offered my choice of ANZ J flights from SFO/LAX/YVR to AKL.
In early December I booked 2 x LAX-AKL in J for a relative departing on December 23rd.