You are a very strong candidate. You have a legitimate chance at any of these schools, including your reaches. That said, schools like Rice have very low acceptance rates even for highly qualified students like yourself, so you were right to make a balanced list. I don’t think there is anything you should be doing to try to make your application stronger. Keep following your true interests.
A bigger barrier is going to be cost. I would definitely continue to research the National Merit schools. I agree that Tulsa might be a terrific choice, especially as the new president is really trying to recruit National Merit Scholars (projected 15-20% of incoming freshman.) Fordham in NY is also a National Merit school. It doesn’t offer Korean, but does offer a number of majors with an international focus and a study abroad at Sogang University. OSU belongs to National Student Exchange, which would allow you to do up to a year of exchange at any other school in the program paying only what you would pay at OSU. There are some NSE schools that have good Korean programs. Alabama is also a National Merit school with a Korean program. It also belongs to NSE. National Student Exchange - Campuses / Location