unique engineering case

Hi, I am interested in applying to engineering programs at the following universities: Georgia Tech, Purdue, UT Austin, WashU, Michigan, Carnegie Mellon, and Penn (possibly Caltech).

GPA:
I am transferring schools for my senior year (from a private all-girls Catholic school to a private coed secular school), which makes this a little tricky as the scales are different. I have gotten all As (4.0/4.0 scale, no weighted scale) and have taken all honors/AP courses available to non-seniors at my former school. In an effort to take AP Calc BC and AP Physics C Mechanics next year, I am currently taking Calculus 1 at a local university.

Here are some stats:
ACT December 2017 (no prep)
Eng: 34
Math: 34
Rdg: 32
Sci: 34
Essay: 9

I took the June 2018 ACT but my calculator malfunctioned so I took the test without one. I am not sure if I should take the test again or if I should send in both score reports with a note about my calculator.

Eng: 35
Math: 29
Rdg: 35
Sci: 33
Essay: 10

I took the June 2018 SAT Math 2 subject test and have yet to receive my scores. I am planning to self-study for the SAT Physics subject test, but want to see if it would be realistic for me to get into schools such as Carnegie Mellon first.

ECs (have done these all three years so far):
Varsity Cross Country and Track and Field (several all-Conference and all-District honors, six sportsmanship/effort awards)
Founder/President of Winter Running Club
President of Symphonic Orchestra (two years), member for three years (I participated in a State-sponsored Solo and Ensemble Festival, 2x all-District performance and 1x all-State)
Three choirs (liturgical, audition, and regular) (1x all-District 1x all-State)
NHS
Varsity Scholar Bowl Member
Diversity Club
Note: my former school did not offer a math/science club, so I was not able to participate in those activities.

Demographic/Misc stuff:
I am a half-Japanese female who is fluent in both English and Japanese. I’m a dual citizen, and I have spent about two years in Japan. I attended a Japanese language school for 11 years (on the weekends) and am up to grade-level for Japanese (I attended public school in Japan over the summer for 7 years). I am from St. Louis, Missouri. I have been contacting the coaches at Carnegie Mellon and Caltech about running in college (not sure if that gives me a bit of an advantage). I attended a summer pre-college program for 7-10th graders for four years (Duke Tip).

Two-time silver medalist for the National French Contest. I did an independent research project on protein-derived bioplastics, and I intend on submitting my project as part of my application. I am generally a decent writer, so I am not too concerned with the essays.

I plan on majoring in either mechanical or aerospace engineering with a possible minor in vocal music.

Here are some questions I would like your opinion on. Based on this information, do I have a chance at the above institutions? Are there any other schools I overlooked that I should be looking at? Should I take the ACT again?

Thank you so much for your time.

I hate to tell students to spend more time on standardized tests, but I would avoid having to tell the “my calculator malfunctioned” story if you can. It’s just one more quirk to your application that you don’t need. Though if you’re applying to schools that automatically superscore you may be okay.

CMU is strong in both engineering and music, but it may be difficult to combine the two - the Conservatory is quite separate.

You might take a close look at University of Rochester. This is a really wonderful place for a STEM student to study music performance and get a minor or double-major; and it’s also D3 for athletics. (Japanese language/culture offerings are extensive too: http://www.sas.rochester.edu/mlc/courses/jpn.html )

Other options with top-tier music and top-tier engineering include Johns Hopkins/Peabody, Northwestern/Bienen, USC/Thornton, Vanderbilt/Blair, and Rice/Shepherd. However, I would group Rice with CMU as a school where the barriers to combining music and engineering are significant. (Of all these, only Hopkins is D3.)

Michigan would be a great choice too, and it’s also strong in Asian languages.

Harvey Mudd could be worth considering - there’s not conservatory-level music but there are solid opportunities through the Claremont Consortium, with the highest-level choral ensemble being the Pomona Glee Club. (There’s also a vibrant consortium-wide a cappella community if that appeals.) Private instruction with voice faculty is offered for course credit. There are quite a few serious musicians at Mudd, and it’s also excellent in terms of a gender-balanced population and culture in STEM. The consortium also deepens the offerings in Asian languages and cultures. It’s also a good place to run D3. (Claremont-Mudd-Scripps joint athletics.)

Of all of the above, Rochester/Eastman jumps out at me as hitting the sweet spot for all of your interests as well as being a slightly less reachy admit than the others - I think you’d have a good chance of getting at least a small amount of merit aid. Very much worth taking a look.

I think you will be a competitive candidate. Look at adding some safeties to your list.