Clarify point/award transfers
Please help me understand or tell me what I'm doing wrong.
I have 113K points with Chase. I need to go to Melbourne, AUS next spring. Dates are flexible. I've missed the opening rewards opportunity, so I'm watching for reasonable fares I can use some points with money. Here's an example of how I get frustrated. I see a nice looking deal on Air New Zealand in Premium Economy. I don't have any point with them directly. Chase does not transfer to them directly. However, they are a part of the Star Alliance, as is United, which Chase does transfer directly to. I thought the strategy is to go to United and search for a flight that Air New Zealand operates, book that ticket after transfering my points to United. The problem is I never see the flight LAX-MEL operated by Air New Zealand because United has enough of their own flights on that route.
Am I understanding how the process works? Am I missing some search option to see Air New Zealand flights on the United site? Will this never work because United is "too big" with it's numerous routes? Will this never work because United is the only member of the Star Alliance that Chase transfers to?
Thanks for any help you can give me, including tips on getting to Melbourne from LAX. :-)