tfung,
salt is correct and according to the rules you would need to go to Oz before you touch Asia again. A second intercontinental arrival in Asia would only be permitted if you were heading to Europe from the SouthWest Pacific.
However, I would bet that if you had a ticket issued SouthAmerica - JFK - SYD that CX would happily accept your JFK - SYD coupon on the JFK - HKG - SYD route. We all seem to have differing experience with each of the carriers and I have found that CX is the most loose when it comes to giving First Class passengers what they want especially if it means they will be taking business away from the competition.
rich