You know you get up to 15 segments on an AONE ticket?
16.
I can see the JAL flight from NYC to Tokyo on the OneWorld planner. It may not operate on the day you are checking. But if it does and you can't see it online, you should still be able to book it on the phone.
JL is pretty stingy with A availability. I'll put my vote with those who recommend CX JFK-HKG. You won't be disappointed with the flight. And you can use one of your unused segments HKG-NRT/HND.