A direct Korean Airlines flight would seem the most obvious, but it didn't depart until late in the day and arrived at 8:30PM, the same time China Airlines arrived. There were multiple options such as China Airlines via Taipei, Korean Airlines direct and China Eastern via Shanghai.

Much to my surprise Delta Skymiles had the best deal and availability. Much more availability was out of Gimpo where I could easily have taken the subway from Incheon, flown to Haneda then taken the train to Narita where I was staying, but this is Reward Flying not Reward Trains.

Using Avios got me to Narita on a Japan Airlines 737, but availability was not certain. The least expensive ones were using 15,000 BA Avios or Delta Skymiles. Returning to the issue of getting from South Korea to Japan, there were a lot of options.