i think Asiamiles award (MPO) does allow for stopover. but it probably cost you 250k miles to do jfk-hkg-akl.
with AA, not only jfk-hkg-akl is possible. you can actually connect to JFK from any US port. e.g. mia-jfk-hkg-akl (though the totally # of stopover is probably still limited to 2)