Looking at the language in your post, you are either not in Korea yet or have not started the position where you are expecting to have lots of desk warming time. I think going for another degree is a great idea, but I do have a word of caution- don't count your chickens before they hatch. While it is true that PS teachers frequently have desk warming time, I would not count on using that time to get a PhD. Until you know what is expected of you by your school as far as lesson planning and teaching afternoon classes go, I'd be careful investing too much time or money into looking into this issue.
It is true that you may have tons of extra time at your desk to do what you would like, but it is also a real possibility that you will have extra responsibilities at your school or have to teach afternoon classes that take up a good portion of that time. Some schools will be fine with you working on your program during school hours, but others might have different exceptions for how you spend your time or even actively discourage you from this type of work while you are at school.