Duke vs Washington University St. Louis vs Columbia vs Rice?

Hello, I am currently trying to find one reach school that I can apply to, and am looking for a university with good prestige, and an actual chance (even if minute) to get in with financial aid. Hard, I know, it’s why these schools are my reach haha. As such, I would like to only apply to one university, and was wondering which ones I should apply to?

My Stats: International Student (Will apply for financial aid as well)

Major: Electrical Engineering// 2nd Choice = Mechanical Engineering
SAT I: 1410 superscored (on the low end)
SAT II: I don’t think it will help my application, so I’m planning on not submitting them, but
Math = 690
Physics = 640
IB Diploma Program (Predicted grade in parenthesis): HL Math (6), Physics (5). Econ (7), and SL Spanish (6), English Language & Lit (7), Chemistry (6)
GPA: 4.13 Weighted (out of 4)
Class Rank: N/A
Essays: Pretty solid, counselor loved them, and I showed it to a few alumni from my school just for some feedback, and they felt it was solid too!
Teacher Reccs: Pretty solid, all were close teachers, and really highlighted me well.

ExtraCurriculars:

  • Varsity Soccer
  • Junior Varsity Volleyball Captain
  • Conducted Research in Universities over summer (talked about this a lot in my essays)
  • MUN Vice President
  • Debate Captain
  • Community Service club founder
  • Won a lot of national and international awards in debate
  • Varsity Badminton Team