I hate to say "ask the ATF," but that's what I'd do. Call them, explain and see if they know what the process is.
One thing to keep in mind however.
The ATF is notorious for changing their mind and/or telling you something when they really have no clue at all. I suggested calling as they might have dealt with this before regarding a form 6 since a lot of international flights come into JFK. I'd also ask to speak with a supervisor or agent assigned near JFK and get it in writing.
I know that wasn't too much of a help, but let us know how things go!