Originally Posted by
Dalewood
So just showing up three hours early for regular check-in with the CC in question will not suffice??

I don't think the OP can easily go to the airport that early. Plus, doing so would be a big waste of time.
A solution (which wastes even more time, but not on the day of departure) would be to go to a DL counter at an airport some days before the flight, possibly LGA (or HPN, EWR etc.) instead of JFK if that would be more convenient.