Very interesting story. I think the depth of it will go a long way. Your work experience sounds strong in the sense that it's consistent. If you've been consistently promoted over the 4 years and taken on increasing leadership responsibility, you should be solid there.
In terms of academics, you are right that your GPA is a big weakness. You should definitely address this in an optional statement and take responsibility for it. You should also show your growth, etc. during and since that time. You probably gained some perspective over that time that you might not have gotten in the classroom, but you have to also accept responsibility for your actions/consequences. Still, it'll be tough to overcome. Glad to hear you took a class and earned a 4.0/A in it - that'll help. Hopefully you can knock the GMAT out of the park; if so, that'll also help compensate for it. Definitely have your recommenders point out your analytic capability, too.
Extracurricular activities seem limited and community seems active but perhaps not in a leadership role (to date). But still, the consistency in the volunteer position over the past couple years will pay off.
All in all, I'd say the things you need to address are your low GPA and your lack of extracurricular activities/non-work leadership positions. You may be able to do this through your personal stories (seems like you've overcome a fair amount of hardship and might be able to develop some great character stories that help show WHO you are versus just what you've done). Make sure you come across as a multi-dimensional candidate (not just education person).
GSB, HBS and Tuck are all incredibly competitive (as you likely know). I do think GSB and HBS will be reach schools, but if you really want to go, you should keep one on your list and give it a shot. Tuck has one of the lowest acceptance rates (given their low class size)... it might be safer to swap this one with a different program. My suggestion would be Kellogg, Duke, Darden, Cornell, and maybe one safer safety like Georgetown. Not sure if Kellogg is of interest to you, but given your interest in education, thought it could be a good fit and slightly more within reach. If not that, then perhaps a different but comparable school.
Hope this helps!
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