Honestly, I think you have a strong profile - you'll be in the running for all the schools you listed.
With a strong GMAT, stellar GPA from a good school (top public, I'm assuming its UCLA, Cal, Texas, UVA or Michigan) and a dynamic/accomplished undergrad experience, it's clear your "raw goods" are comparable to your peers at comparable schools who may have taken the more conventional path (mgmt consulting, banking, Google, etc.). In other words, in a parallel universe, you probably had the college resume to go the conventional blue chip route (McKinsey/Bain/BCG, etc.).
But you took a more unconventional route - eschewing the what your peers may have done.
So you are the classic vagabond - the person with a solid blue chip undergrad foundation, but who took the road less traveled. You are basically comparable to that Princeton alum who rather than worked at Goldman, decided to work in fashion, or do social enterprise work in South America, or something like that.
And people like that do get into the top schools you listed.
In your case, it's not about trying to "stand out" (because your profile will naturally make you stand out) - but convincing the adcom that you can "fit in" with all the other cookie cutter McKinsey folks at HBS (or any other school). So it's about how well you execute the applications.