Hi Emily,
I'm guessing you were teaching at a hagwon. After my first 12-month term, I asked for the return fare equivalent in cash and put it towards my visit to Northern Europe. I was with one of the rare good hagwons at that time. Then I returned to another school. If your boss is reasonable, there should not be such a time limit. If you fulfilled your 12 months, it's payable.

My observation is that with Koreans, it's pretty much "Out of sight, out of mind." I would get closure first and take the cash equivalent.
Also, I don't know who Theo is, but what he writes is TRUE. Contracts are non-enforceable by the Labor office and Courts laugh them off.
Personally, during my 5 years in Korea, when I worked for a good school, and they are few and far between, I was in heaven, but generally, their word means nothing and the contract is not worth the paper it's written on, so don't take promises and deadlines too seriously.