Wow, this might be the most detailed post we've ever received! Hard for me to do justice to it all in this space, but I'll share a couple of thoughts:
The fact that you finished your undergrad work in 3.5 years (plus the internship) is impressive, but it probably won't matter much at the end of the day. The thing that jumps out at me as most interesting there is that you scored a somewhat unique-sounding internship, and the company liked you enough to keep you on for more than just a summer. The AP credits and all of that don't really matter at this point.
Lots of good undergrad involvement, but as you probably know, your involvement since then really starts to matter more. I understand your challenges re: getting involved since you move around a lot. Focus on your internal GE involvement (e.g., March of Dimes) as much as possible over the next six months, to really have some great achievements to point to.
Great work experience, from what I can see here... Of course, GE itself is a great name to have on your resume, and it sounds like you're been doing real, serious, important work there. The more examples you can provide of gaining increasing responsibility, going beyond your job description to make things happen, etc., the better. (This is part of what we help our clients do!)
Yes, definitely try to get that GMAT score above 700, just so that it's not a weakness in your application. I wouldn't say "Don't bother applying to HBS/Wharton if you don't break 700," but I would take your retake VERY seriously.
Additionally, I do think you should think a bit more broadly than just HBS and Wharton! With a great GMAT score I think you should indeed apply to those schools, but, esp. if you're on the fence and could go into consulting or PE, maybe also look at Stanford, Kellogg, Chicago, and/or Columbia.
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