courier

The SOP doesn't have to be amazing, just competent (i.e. you can detail your academic and research experience and state a few potential research areas of interest). The letters of recommendation, grades (especially those in upper division math classes), and the general GRE scores are the most important parts of the application. The GRE is mainly a filter though, but a high score on it can sometimes lead to on-campus fellowships. Your GRE scores are exceptional -- even better than a lot of domestic applicants (the GRE V score is certainly very impressive for someone whose first language is not English).

Given that you are from one of the top 3 schools in South Korea and your overall grades in math/stat classes are pretty good, your list of schools is very reasonable. You do have a few B's, but most of your other grades are excellent. I don't think you need to worry so much about the fact that you switched from business to stats. I know people from South Korea whose undergrad major was business (they only took math courses in their last few years so they could apply to Stats graduate programs in the U.S.)
UNC-STOR may be hard to crack, though. This department is tougher to get into than the others you listed, and furthermore, it is also more probability theory-focused than others. I would recommend you apply to NCSU.

I was in your situation this past cycle, but more severe. The only stats course I took was 101 freshman year. The rest of my courses were pure math, like logic, algebra, and analysis, not even probability! I still got into some great programs. At visit days I learned that it's far more common to have a pure math background, although typically students have seen some level of mathematical statistics, so I do think I'm still in the minority, but I'm not quite as odd of an applicant as I initially thought. A professor at UW explained to me "we look for people that can learn statistics", as opposed to people that know statistics.
 
So, a background in pure math + graduate statistical theory class + research in probability and random processes actually makes you an ideal candidate from what I can tell.