If I was in your position I would do some research in S. Korea regarding 'international exchange students.' At the university in China where I work we have lots of these students. They have their own dormitory building which is close to a Chinese/Korean campus restaurant (actually the best place to eat on the campus, although more expensive than the other restaurants).

We have at least two S. Korean teachers, (those I have met anyway), who teach Korean and English. We also have a professor who previously worked for a very large and internationally-known S. Korean company who teachers business English, and another who teaches translation.

Perhaps you should focus your search on universities that have schools of foreign languages where your fluency in Korean may be an asset.

Turnoi has a fair point about seeking work in Europe, although for the better positions (professor level), there are Koreans employed but usually these individuals have a PhD and often work in science related fields.

Incidentally, it would be a good idea to get some TEFL certification.