Hello and thanks for your post.
The application process is truly holistic, and committees will look at your stats (GPA and GMAT), work experience, and extracurriculars.
Your GPA of 3.87 is strong, so that is a good start. Your GMAT is also strong, though it is slightly below the average for the schools you mentioned. Retaking it is a good idea; 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. 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 (though I don’t think a course is necessary given your profile).
It is hard to gauge your work experience without knowing your accomplishments and impact you have made there. It is nice to see that you have already been promoted. It will be important to show you have made an impact and demonstrated leadership there. 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. I also agree that a short-term goal of PE/VC will be tough to sell to admissions committees.
Regarding extracurriculars, make sure to really emphasize your leadership roles you have taken on. Acting as a mentor sounds impressive; that is one aspect of your profile on which you can elaborate.
If you continue to strengthen your profile, you do have a chance at some of these schools, but they are extremely competitive, and each school simply does not have the room to admit all the world's qualified applicants. For that reason, I suggest apply to a couple more schools, including reach, target and safety. But with a very strong application, you have a chance at even your reach schools. Hopefully they will see that you have a compelling story and are someone who will add value to the classroom and community.
If you would like to discuss your story or anything else in greater detail, please sign up for a free consultation or email
Michael@mbaMission.com.
Good luck!