Via Point Me to the Plane, Air New Zealand business class from SFO, LAX, and a bit less so out of IAH are widely available to fly nonstop to Auckland (AKL). I was able to find a good amount of availability from SFO for the next few months.
It doesn’t look like continuing awards from AKL to Australia on Air New Zealand are very open though.
Via View from the Wing, JAL First class space is also widely available between Tokyo and Sydney from March to December this year.