Thanks for the information. I've actually taken the Korean Air flight from Aomori to Seoul when I used to live in Aomori. The only problem is that the flight only operates 3 days a week. Also, when I check the flight schedules between Tokyo and Aomori on koreanair.com, it just lists the JAL flights.

At this point, I'm starting to think about taking the train. It'll take four hours, but I can get a railpass for only 20,000 yen.