[Nathan]

I don't know about the JET programme, but there is another alternative for your Masters (an option my uncle keeps trying to push me towards).

My uncle has been an English teacher in Yokohama for 15 years, at the university level currently.

If you really want to pursue ESL in Japan, you could get one with just your Bachelor's degree. Try to find something within the Kansai area, and apply to get into the Temple University branch in Osaka for your Masters in TESL. It's a bit expensive (around 2,000,000 yen last count) over 2 years, so you most likely wouldn't have much of a social life between work and school. But it would make paying for it slightly easier since you'd be making money at the same time as studying.