I'm in the same situation (trying to go NYC to AKL) and I've looked at all of the routing options, however, what I haven't been able to find is if Oneworld Awards are pulled from a separate booking class/inventory than normal Aadvantage and Aadvantage Partner awards?

Since the OneWorld awards typically cost more miles, does that mean it's a different booking class? Or is the extra mileage you pay only for the luxury of multiple stops, airlines, etc. Thanks.