And just another tip for EF (for clarity) - search specifically (and only) for the transatlantic flight leg, don't include your O/D airports. Search for direct only and exclude codeshares. This will help you filter out a lot of the junk.

As others have said, your odds will be better (though not necessarily outstanding) for JFK-FCO. Or if you want to maximize your odds of an upgrade, something routing JFK-LHR will have a decent chance of clearing due to increased daily capacity. Of course, this requires at least 2 connections and juggling your connecting flight options.