Originally Posted by JJeffrey

Since you booked the award through AA this doesn't have anything to do with what JL will or won't allow, but just AA's award rules. AA does not allow stopovers on awards, so it's not possible to fly KIX-HND, stop for a few days, then HND-JFK on the same award.

Also because KIX-HND-JFK is a partner award, and HND-JFK would be just an all-AA flight award, I do not believe it is possible to just drop the KIX-HND segment and keep your existing HND-JFK for no extra miles.