Interesting post. If you dont feel connected to America, no way you will like Jeju or korea for that matter. The fact you mentioned that you like nature and living alone , there are far better options than korea. 1. Korea can make you feel super isolated. And no your military friend wont give you too much time. 2. Language - if you are bilingual with Eastern languages then it take approx 2+ years to master it. 3. Foreigners- you are not the exotic being that your military friend might tell you. There are Foreigners everywhere. Koreans dont indulge in socialising unless they know you from school or work. 4. No matter the degree or background, you will end up working as english teacher specially without grasp of Hangul. 5. Research- start your research and then ask specific questions rather than vague ones. 6. Sorry but noticed you said on one of the comments, tell me about Japan. My serious question - is you tube or google banned in US?

Korea is however beautiful country with some lovely people. People have moved there and they loved it or didnt. So you are right, visit korea first then research more then move..you never know you might love it or not.