How can I advance my English skills as an already advanced student of English?

Practice, practice and more practice. You've already learned all the grammar rules, gained a large vocabulary and become confident using the language, so all that's left to do is practice.

I know this isn't the magical answer you were looking for but it is the truth. The best way to practice is also quite obvious - move to an English-speaking country for a year or two and communicate only in English. Ideally do some work while you are there that requires you to speak, read or write as much as possible with as many different people as possible. Living in a country where they speak English natively will allow you to perfect the language to a level that would be otherwise incredibly difficult to achieve.