I think there are two ways to look at 'unique-ness'. The first is the way you're looking at it (the glass half-full method): you're unique because no one else has similar profiles as you; therefore, you stand out among the thousands and thousands of applications that, for example, HBS sees each year. The other way, or the glass half-empty method, is equally valid - why should adcoms risk their chance of admitting you when the next guy that graduated from UPenn, worked at JPMorgan's advisory department for 3 years (+ a promotion from analyst to associate), with a solid 3.7 GPA and 710GMAT, is applying to HBS? This is an important distinction that one has to keep in mind. Is being unique really all that great? Can this 'unique-ness' translate into transferable skills that the applicant can use when going through recruiting? Keep in mind that b-school rankings are not just based on GMAT and GPA, but employability. To admit someone knowingly that he/she can't get a job is like trying to revive a dead horse. So enough with my weird metaphors.
I think you do have a unique profile and that you do have a shot at getting into top 10. However, really keep in mind that no one's a shoo-in for such a competitive environment anymore. When you look at the 9000 applicants to HBS or 5500 to Kellogg (I made up those #s, don't hold me to them), some will bound to be non-traditional, or 'unique', thus the real question is how does one stand out from the unique of the unique? That's one of those questions that cannot be answered. On one hand, it's too hard and ambiguous. On the other, it seems almost too easy - you're already unique!! My point here is that while you have a shot, also keep in mind the type of mentality that all other applicants have. One will certainly argue that everyone's unique and that's true to a certain extent. Bring out your own specialty in your application and craft those essays with an intent. With your verbal score, I'm sure you can kick those essays ass easily. Good luck! This was a long-winded answer and isn't warranted, but I just kept on typing and typing.
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