I'm wondering whether I can get into my college of choice with a mediocre GPA and a fantastic SAT score (I don't know how much that would be… 2100+?).

Yes you can.

What will be even better is if you are allowed to write some kind of personal statement.

As a current graduate student, I can say that after 6 years of college (so far) the only thing that's reinforced is doing well on tests. The stuff that really matters in the real world cannot be taught in a classroom, like how to really get ahead and make money. You don't achieve this by being nice and playing by the rules.

You just have to play their game for now until you can get to a point where you call the shots. It's worth it even though it might be painful at times. Good luck, start thinking about your major immediately.