Just a heads up, you can book on Expedia.IT and potentially not fly the last segment without repercussions and even check in luggage.
Article from The Sun and
Italian Competition Board Decision
Per a local regulation you can fly the segments you want and they can't force you to reprice or anything if the point of sale is Italy.
Not for everyone, if trying Hidden City then just do carry on or force an overnight stay in JFK.
But if you are brave and book on an Italian OTA , keep the document on the case you could even use it for a LAX-JFK round trip cutting out the JFK-KIN...
Expedia Link