Hello OptimisticApplicant, thanks for your question.
I do think HBS and Sloan could be reaches for you; I think you could be competitive at Babson.
Your GPA is a surmountable obstacle if you frame the circumstances in an optional essay and because of your other academic performance and GMAT. If you do write an optional essay, make sure that you call out the truly unique circumstances you faced. There are lots of student athletes who are chemistry majors at top-notch schools who have stellar GPAs, after all.
I think your competitiveness will come down to the quality of your leadership experience in and out of work. Can you draw upon "moments" when you truly led: influenced individuals and organizations, drove results, took initiative?
In terms of extracurricular activities, what you've done more recently has more weight than what you did in university/school. The more you can call out your leadership in these roles you mention, the more competitive you will be.
Finally, in terms of your post-MBA goals, paint a picture that cohesively ties together your past, present, and future. Demonstrate to the admissions committees that your desired career path necessitates an MBA. It seems like you have some entrepreneurial experience - why would you need an MBA to continue that path? Why not stick with your startup? These are questions the adcoms will want you to answer.
I hope this helps!
Best of luck,
Brian
