Ah that's right for the oneworld you need 2 carriers. So you could go LAX-AKL-SYD on Qantas and SYD-NRT-LAX on JAL and still be <20k miles for 130k points

It looks like any way you do it going to all 3 is going to be in the 170k-190k point range

If you want to keep it simple and get a lot of flying out of it (but a few more points) you could take lan to ppt and back to scl and across to akl-syd-lax. That should be 190k points and you would actually have ~6k miles left over if you wanted to go somewhere else.