I agree with the suggestion to apply to Caltech and MIT EA, unless you have a very strong preference for Princeton. I’m prejudiced, of course, as I have lots of parental knowledge of these 2 schools.
You have worked very hard. It has just gotten harder to get into these Universities. You are fortunate that tuition cost will not be a hindrance.
I’ll get right to the point:
You’re in at whichever school needs a cellist.
The meal plan at Caltech worked well for my son. The Houses often had food on weekends, and clubs brought food in. He rarely spent more than $17 on weekends. It was also nice to live in a House throughout; no eating clubs or Greek life.
Cambridge can also be expensive, but the boys lived a distance from the T-line, found good and inexpensive places to eat, and learned to cook with delivered meal packages.
Internships paid well, and son took on jobs during the year.
I suggest starting a “so-called prestigious schools aren’t worth it” thread rather than starting the same conversation/argument with every student who simply asks an admissions-related question.
Ignore those that say your chances are the same as the average applicant. You have a good chance of admission to at least one one of those schools as long as your recommendations are strong and your essays are good.
But importantly, a good chance of admission does not mean a guarantee of admission. So you need a solid set of match and safety schools. For a moment, I will skip discussion of the safety and come back to it later.
I recommend applying EA to MIT, CalTech, and Michigan. For Michigan, apply two weeks ahead of the EA deadline, as they often get too many applications to give all of them a decision in December.
If you get good news from MIT or CalTech, you might decide you are done, or you can apply to Stanford or Princeton for RD if you choose. If you only get into Michigan, you have a solid base upon which to add other schools for RD. Possible colleges to consider include Vanderbilt, Duke, Penn and Cornell in addition to Stanford and Princeton.
And in the unlikely event that all three defer, you need to apply to a full range of schools including your safeties. Now, what are your safeties? You need a good plan for that.
By the way, what is the status of the research project? Is a paper likely, and will you be an author on that paper?
Note, I NEVER say prestigious schools aren’t worth it. I only reply when posters say “cost is not a factor.” It’s to educate on the true impact of the cost difference, so THEY can determine if it’s “worth it” or not. Any devolution is based on others chiming in with evidenceless arguments justifying the expense.
Being an Asian male in STEM (particularly from a state like NJ) does reduce OP’s chance of admissions relative to any other group. However, OP still has a better than average chance of admissions, particularly at Caltech (where race is less a factor) and Princeton (where OP’s state of residence isn’t as big a handicap).
Thanks so much for all the feedback!
Yea unfortunately next year is the first year that my school will offer any math class beyond Calc BC, and I actually had to push the math supervisor to add more classes as there was no teacher willing to teach the class. I couldn’t do much about that besides self-study some topics which obv can’t be officially recorded on my transcript.
One thing I was rly proud of was successfully connecting soccer and math together into one project that made it to ISEF. I will definitely highlight my pursuit of these passions beyond the surface level. Also, in order to bolster the advanced math, I do plan to further progress with my graph theory project: hopefully getting a published paper out of it.
Thanks so much again!
Thanks for the feedback!
I thinking a similar plan for early admission. In terms of safeties I hear that Purdue has quite a strong Math department, so I will def look into that.
For the soccer research project, I published a paper through JEI which is essentially a journal for student papers. Not the most eye-catching publisher, but its something.
Then for the graph theory project, I’m currently working on getting a paper out with a more established journal. Hopefully that goes well.
I was the first author on the first paper and plan to be the first author on the second paper.
Haha unfortunately orchestra conductors don’t hold that strong of an influence over admissions.
Nah I’m on varsity but I’m basically just good enough to get some playing time here and there. Play soccer cause its fun, I get to mess around with my friends, and get some exercise at the same time. win win win situation
Neither MIT nor Caltech are soccer powerhouses! 
If it gives you an edge, use it. 
I would bet that soccer at Caltech would be happy to have you. It’s hard to field a team that can score 1570 on the SAT. You’ve got the stats to get in, but soccer be the difference maker. It’s worth communicating with the coach and testing the waters.
I sat in an east coast information session where the director of admissions said “If you’re from North Dakota or play the oboe, please come see me after the session”. You never know.
Thinking about this a bit more, another reach to consider is Yale. If you don’t think Yale when it comes to STEM, well, that’s exactly why they actively recruit strong STEM kids unlike all of your other listed schools.
Another match for you is NYU. Its Courant Institute for mathematics is world-class, but NYU has easier admissions than most schools on your list.
And a safety for you is Stony Brook. Its strong math program was once run by James Simons, the hedge fund billionaire, who still maintains ties to the university.
Agree about Yale. Pro-tip, look up the recent revamp of the Yale math intro sequences, mention it in your application, Yale math is on the move and for sure has been actively seeking out strong math students. You’d slide perfectly into the honors linear algebra/intro analysis sequence as a freshman - it was designed for strong aptitude math students who might not have had much prior exposure beyond single variable calc.
Just to add some more ideas, U Michigan has a terrific honors math program. Also, consider U Chicago for an ED2 if your early round choice does not work out. Fantastic math program, unlimited course selection, extremely strong math students, if not at the IMO Gold level of the top group at Harvard and MIT (which can actually be a good thing for the merely mortal students).
Do you actually have a preference for any of these schools or do you just want to maximize your chance to get into one of them? Do you have any idea what you’d like to do after undergrad?
Agree with the testing the waters. However, Caltech and MIT coaches will tell you full athletic support only gets you to 50/50 assuming you are academically qualified.
OP, agree with the posters above that your chances are way above average given your qualifications, even being an ORM. As for which school(s) to apply EA, I’d base it on what is your first choice school. The schools on your list are very different and will offer very different experiences. The REA schools do allow you to apply to publics early/rolling. I am a big fan of applying to matching publics early along with a top school to hopefully secure at least 1 acceptance by the RD deadlines. This will help narrow the list and reduce apps to prepare and pay for.
Out of the 4 schools listed, MIT is my favorite by quite a large margin. However, I would be ecstatic to attend any one of them.
After Undergrad, I currently plan to pursue a PhD, but that is not something I am deadset on.
Will definitely look into Yale based on what you and @hebegebe have both said.
UMich and UChicago have also been on my radar.