The most important recruiting measurables with Univ of Chicago is going to be your grades, academic rigor and SAT/ACT scores. Very difficult school to get into with or without baseball. If you currently have desirable academic numbers for the Univ of Chicago and it is your top school, why wait? Try to start a dialogue now with the coaches in advance of HeadFirst or other academic showcases. Take the initiative.
Over the last 4 years, I've known a couple people that were seriously recruited by the Univ of Chicago. Both loved the campus and liked the Coaches a lot. Both had extremely complimentary things to say about the school and the program after their sons visits. I was led to believe the Coach has a little "academic latitude" with 1-2 players per year with Admissions, but not a lot. This is why it is so important that you start a dialogue with the coaches to find out exactly what it is they are looking for, and if you have what they are looking for.