I'm not familiar with Korea, but I do know that you cannot get a legal teaching job in Japan without an undergraduate degree (in any subject).

Also, manneca is correct. If U.S. citizenship is your goal, then you should stay in the U.S. until you accomplish that. Going to a third country for any significant length of time could trigger a requirement to start the process over.

You'd be 28 when you received your citizenship, still young enough to qualify for a student visa in Japan, although U.S. citizens are not eligible for Working Holiday visas.