Hello and thanks for your detailed post.
The application process is truly holistic, and committees will look at your stats (GPA and GMAT), work experience, and extracurriculars.
Your GPA is strong, so that is a good start. Your GMAT is good too, though compared to others in your demographic, it is below the average for the five schools you listed. If you haven’t already, I suggest taking it up to 3-4 times. You have nothing to lose since schools will only look at your highest score. And even a slight increase can boost your profile. You may still want to illustrate to the schools that you have the academic ability to succeed in the classroom. For example, you could showcase your quant ability in your resume, your recommenders could do the same in their recommendations, or you could even take a supplemental course such as stats or calculus.
Your work experience looks impressive, and it seems like you have been a part of some important accomplishments there. It is nice to see you are a top performer on your team. In your application, make sure to show your impact and all of your leadership and initiatives. Ideally this will be supported by strong recommendation letters as well. It will also be important to explain why you want your MBA, and to also illustrate the skills you already have which are transferable. Be sure your story makes sense, and is realistic and specific.
Regarding extracurriculars, make sure to really emphasize your leadership roles you have taken on. It is great that you have taught underprivileged children. And you can certainly mention – perhaps on your resume – your anecdote on completing the half marathon.
I suggest apply to a few additional schools as well as the competitive schools you listed. In general I recommend applying to reach, target and safety. Hopefully they will see that you have a compelling story.
Good luck!