Hi,
Sounds like an exciting choice!
You mentioned that you are taking college level courses in a few months. Do you have your bachelor's degree already? A 4 year bachelor is required to get an E2 visa to teach.
If you don't have your degree but are determined to stay in korea while you get your degree, you could always teach private lessons (which are illegal) while you get your degree. But this would require you to do visa runs to Japan every 90 days which may look suspicious after a few of those trips.
If you don't have a degree, another option to stay in Korea would try to get your degree at a Korea college so that you can get a student visa and be more legit in terms of your stay in Korea.
Lastly, if you have a degree, just start looking for jobs in the town where your fiancee is. I'm sure there are plenty of
ESL jobs around in your area.
Eric