I'm tilted towards Star Alliance, since I've had pretty good redemptions with UA as long as dates are flexible. The drawback is you may gave to purchase your domestic flights within Australia. Otherwise you can do something like SFO/LAX-AKL-PER then SYD-LAX/SFO. I've also seen some circuitous routings like SFO-TPE-BNE on EVA (BR) or SFO-SIN-PER on SQ or LAX-BKK-PER on TG. Another option is to do a semi-Circle Pacific routing using two one-way awards, such as LAX-AKL-SYD then PER-SIN-NRT-LAX.