Based on your academic background/performance and GMAT, it's a given that your a very bright guy. Also, unlike the stereotypical "propeller head" you seem to have experience and skill in interacting/working with other people.
The bigger question isn't whether you have decent or even strong interpersonal skills to be a valuable team member (you probably do). It's whether you have strong enough people skills that executives (and eventually, Board members) can tag you as a big boss. Is your biggest potential being the "boss", or being a "valuable contributor"? That is more a gut call made by the adcom reading your application.
Practically speaking, I think you should be competitive for MIT and Chicago. Probably Wharton as well. HBS and Stanford - can you convince the adcom that you're the kind of person who others will entrust with responsibility over lots of people (as opposed to being one of the team members - albeit a talented one).