Use the BE checkin area in T3. It is the only check in area for DL at JFK that I use (I don't know if they open before 2 but you are leaving later). The stroll over to T2 isn't bad at all and is assisted with rolling cat walks. The security line has never been crowded when I have traveled through there.

If you ask me, this is the one of two major perks at JFK. The other being the CRC/BE lounge in T2. In the afternoon, some neat food stuff is placed out for the BE crowd. Because this BE lounge doubles as a CRC, you win/win even when not flying BE. Also, there are a couple of rooms (glassed in) that use to be smoking rooms (10' x 10') which are very comfortable. Last April, my family of five camped out in one of those for an hour, ate...drank...and were merry.