Where to apply early? UChicago vs. Princeton

Hello all, this is my first post, and I won’t sugarcoat anything. I’ll just lay it out straight.
I’m an incoming senior into a very competitive college-prep school that sends roughly 30% of its senior class to ivy league universities. My school college counselor has excellent connections with the UChicago dean of admissions (who is also the person who will be reviewing my school’s applications). My father got his PhD at princeton, but I’m not sure how much that actually matters in undergrad applications.

In terms of grades: (All classes either honors/AP)
Freshman year was a disaster, with mostly Bs and B+s, with a single flat A.
Sophomore year yielded equal As and B+, with one flat B (an A+ in an astronomy elective).
Junior year fared slightly worse, with scattered As and B+s, with one flat B.

I realize this sounds grim, but I cannot emphasize (at the risk of sounding hella cocky) how competitive my school is. Accordingly, my school calculates neither GPA nor class rank.

I’ve taken AP French, Statistics, and English Lit, and have 5s in all three.
SAT 2s: Bio 740, French 790, Math2 800, Italian 780, Physics 700, French Listening 740.
Sat 1: 2310 Superscored, planning on taking ACT in April.

I’ve taken a national (standardized) french exam, and placed 6th (“gold medal”) in the country.
I’m planning on listing French/Italian/English Comparative Literature (or something along those lines) as a major.

EC: Violin at a competitive conservatory, with various prizes in lesser-known competitions around the region, with 2 state-level recognitions.

  • I volunteer at a local city tutoring center to help teach kids math, history, writing, and science.
  • section Editor for school newspaper
  • writer for school literary magazine
  • various internships/independent studies (most notably paid economics internship at Minneapolis Federal Reserve)
  • 2 Jobs teaching at various schools during the summer for 2 years straight
  • language immersion programs in france during the summer for 2 years

I’ve probably left some stuff out, but all the most important stuff is above.

My english teacher had me write the common app essay as an actual essay, and I received an A on it, and my college counselor (ex-admissions officer at Columbia) read it over and changed only one word.

My college list had UChicago at the top, with Brown and Cornell on the list. College counselor did not agree that I should put princeton on my list, in that it was out of my reach, but said he would support me should I decide to apply.

Basically, since the admissions rate differs so little between UChicago and Princeton (.5%, I think), that there’s no reason I should hold back. Of course I’ll apply to both, but the question comes down to which school I should apply early. My writing is fine, so I trust that my essays will be great, and my recommendations will be equally commendable.

SO, the $42,000 question: At which school would I have a better chance of acceptance if I were to apply early?

Actually, as I read this out loud, I should specify. I think overall I would have a better chance at UChicago regardless. But rather:

Do I have enough of a chance of getting into Princeton that it’s worth sacrificing the (relative) advantage that I have (given my school’s connections and higher acceptance rate) at UChicago?

Whether it matters or not, I just remembered:
I’m also the concert master of the school’s honors orchestra, and a president of the “classical music appreciation club” which organizes events to go to concerts around the city.