A non resident can not possess a handgun in NYS for any reason other than for sanctioned competitions ( GSSF, NRA...collegiate ). They do not care if you have a permit for your home state, and they do not honor any other state's permit. Non residents can not apply for a NYS permit either.
In plain english: Don't bring it into NYS, its a felony if your destination is NYS.
The transport law only applies if you are just driving straight through NYS to a state where you can legally possess the handgun, which is not your situation.
Solution: If you simply MUST have a firearm on you at all times: Put an unloaded shotgun in a case in your trunk, and bring ammo in a separate container.
You are the bows from which your children as living arrows are sent forth.