Try UA via SYD in either or both directions as well as HNL. The HNL option will be a NZ 767 HNL-AKL though so not as ritzy as the LAX/SFO-AKL options.
NZ will also sometimes show no J reward space available on LAX-AKL on their flights that route via NAN APW or PPT, but if you break the same flight up into LAX-NAN-AKL LAX-APW-AKL or LAX-PPT-NAN it will on occasions give you a Business Reward seat on each sector. Sometimes. If the Availability Gods are good to you. These options are again on a 767 though.

NZ Business rewards also seem to open up closer to departure date these days, unlike in the past. Maybe you'll have better luck over the next couple of weeks as departure draws closer. I'd suggest AC via SYD as well, but we know that 'aint gunna happen for D space!