http://www.epik.go.kr/contents.do?contentsNo=48&menuNo=275Says here you need to have a teaching license? That would probably make you eligible on the international school circuit as well, since international schools aren't obligated to hire from the 'big 7'. Also, you'd be teaching English Lit, which is a hell of a lot more dignified than the joke that is ESL.
If teaching English is something you want to do long term (I don't see what your alternatives are with an MA in Eng Lit, besides doing a PhD and going the academic route) then I'd (a) forget about Korea, (b) get my teaching license, (c) work on getting my accent as neutral as possible, and (d) start applying to international schools. The only catch is that you might need to take a job in India to build up at least 2 years experience (this is the gold standard in international education). Of course this would have to be at an 'English medium' school (like the one you graduated from) and you'd need to be teaching Eng Lit.
But if you already have a career in mind and you're super intent on sojourning in Korea, just get your teaching license in India and hop over. I heard getting a teaching license in India can be done in as little as a year, depending on prior qualifications. I could be wrong though.