I'm surprised they used only a twin-engined aircraft for such a long flight.
http://www.gcmap.com/mapui?P=jfk-syd&MS=wls&DU=mi&E=330
Try dropping the ETOPS to 60 minutes and you'll be able to clearly see where the airports are.
In practice that means that each type of twin-engine aircraft has a limit: Can only be that far from shore. For aircraft with more reliable engines the limit is higher, so they don't have to pick island-hopping routes when crossing oceans.