You pretty much summed up your options: JAL, ANA (flights may be offered by Air Japan, which is essentially ANA's Asia operations in KIX
), Asiana, and Korean Air. Korean Air would probably be the least expensive but I may be wrong, be sure to check around and look at your options. And with the plane ticket change, unless European/Asian airlines are much more lenient, I wouldn't expect to be able to pull off a free-of-charge itinerary change on a nonrefundable ticket unless you have a real legitimate reason for it (like if the schedules changed and the new itinerary fits you better). Maybe you can work something out with Air France, Korean Air, and KLM now in SkyTeam. Good luck and enjoy your trip.