I think KE flies a nonstop flight in the afternoon between JFK and ICN. It is definitely within the range, but in order to fly nonstop, both KE and OZ have to sacrifice some cargo loads... OZ is using a Boeing 747-400 Combi on this flight... so I guess the benefits from the cargo are better than flying only passengers. KE also picks up passengers from Anchorage on the return segment.
Carfield