Congratz! You know, as much as I bash you, you could craft a perfect application if you work hard!
Then accepted you 1 year in advance though?
I cold emailed my first professor to get the spot. After that, I won the Goldwater scholarship, and my next lab a professor asked me. Oh how the tables have turned haha.
When I emailed the professor, I made a really individual, specialized email for each professor and not a shot-gun letter. I wrote about what interested me in their research and how it help. PM me if you want the email - if I can find it.