If you're already flying EWR-NRT, NRT-ICN-AKL isn't a huge detour at all (600ish miles?). Catch a cheap flight AKL-SYD (there are a ton of airlines flying that route), then fly back SYD-ICN-JFK. It's only a detour for SYD-NYC, really. Or you can catch another cheap flight SYD-CNS, and fly CNS-GUM-HNL-EWR.