The objectivity you mention is exactly why I had considered applying to Cambridge. Ultimately I figured with my application portfolio I would get into at least one American college I wanted to attend (a miscalculation for sure) and that therefore it wouldn't be worth the hassle to apply as an international student and have to acclimatize to another country.
If I do decide to take a gap year and don't (or can't) defer enrollment at UCLA, that would likely be where I'd look first.
Our system seems disgraceful to me because it encourages students not to be true to themselves. I doubt most people that age are truly passionate about many of the extracurriculars necessary to cultivate a favorable persona. I did what I did and didn't do what I didn't do out of a genuine passion for learning about math. I figured that if I did well (even if I did well in my own way at my own thing) admission would follow.
But instead there's a mold I have to conform to.


"The thing that doesn't fit is the most interesting."
-Richard Feynman