Here's the problem and you probably don't want to hear it.
You are:
- Asian-American
- brand conscious
- studious/bookish/academically oriented (high GPA, GMAT, thinking of PhD for a while)
- hodgepodge of extracurriculars that seem more like "busy work" than an extension of who you really are
- orchestra (you'd have to be Filipino to venture beyond classical music)
- research/analytically oriented career path and internships (finance, research).
These characteristics are so archetypal of the Asian-American that the biggest risk you face in the b-school admissions process is that you fail to come across as an individual -- that you risk coming across as a caricature because nothing in the above really separates you from so many of the other Asian-Americans applying (and no, in b-school admissions your strong academics won't compensate for anything - it's not about being "exceptional" it's about being "good enough" with the books).
Regardless, you should apply next year, not this year because one year of the kind of experience that you have simply isn't strong enough for any of the schools you mentioned.
Assuming you apply next year, being completely cookie cutter with your profile may be just good enough for schools outside of HBS, Stanford or Wharton. However, for these three schools you do need to convey something about YOU that goes against the conventional Asian-American experience (and adcoms are VERY well aware of what the archetypal Asian-American experience to the point where they may develop prejudices without even realizing it or being unwilling to admit it).
Again, you could get lucky with H/S/W being conventional, but more often than not the kinds of Asian-American folks I've seen (particularly at H/S) have something in their background that isn't stereotypical:
- single parent (woman) with a lib arts background from a highly patriarchal society (I'll let you guess what country that is)
- gay, bisexual, transgender (AND are involved in LGBT extracurriculars/activism)
- nationally ranked athletics (figure skating, gymnastics, water polo, swimming, table tennis, pro golf, etc)
- arts (anything other than classical music -- could be filmmaker, screenwriter, actor, jazz musician, working at music label, etc)
- community service awards
- culture, religion and politics (significant leadership/service awards in cultural/political activism)
- non-analytical background: lib arts, speechwriter/PR/advertising/arts/nonprofit/etc
- serving in the military
A lot of this stuff goes against the grain of what Asian-Americans have been "pre-programmed" to do from their parents, but that is sort of the point all along - adcoms who see *so* many Asian-American applicants over the years are hoping to see if you have a history of defying the conventions and even stereotypes that have been so ingrained in the adcom offices at so many US universities. ESPECIALLY if you're going into entrepreneurship. They're not looking for a bunch of daredevil risk takers (MBAs as a group are primarily risk averse), but if the pendulum swings way too far in the direction of convention, they'd rather take the person who has some capacity to beat to their own drum.
Sometimes I wonder if I should even write all of this in mixed company (it's an issue specific to Asian-Americans and the obstacles - both self-imposed and otherwise -- that needs to be addressed), but hopefully it doesn't open up a whole can of worms...
I don't want you to change who you are for the sake of admissions or anyone else, but just wanted to make you aware of how adcoms may perceive you.