Put the gun in a long gun locked metal case... I doubt TSA gives a damn about NY law as they are federal. After the guns checked, no one, and i repeat no one at all is allowed to open that case for any reason.
That being said, realize u are breaking the law by driving where u are driving with it, and that being said, an unloaded weapon in a locked gun case...depends on the cop.
Take the gun apart as far as you can take it apart, maybe youll have something to stand on if trouble comes up on some bull**** basis that it was gun parts you had and not a finished product. I know thats some BS, but hey, if you just must do this, thats what I'd do...