No need retake your GMAT. Your GMAT is awesome. Top school GMAT averages are around 710-715. You are above that. At this point an extra 20 points on the GMAT will do little for your application. You need to concentrate on your other elements - your thoughts, your goals, your essays, recommendations, resume. Don't worry, you'll have your work cut out for you!
Secondly, regarding your recommenders. It is a mistake to think that schools want recommendations from senior management and CEOs only. Actually you are fulfilling the most important requirement r.e. recommendations.. i.e. that they be "glowing". Just make sure they are and you will be fine.
Your analysis is pretty on the dot, although I would say you still have a chance at the big three. They key here will be your goals, passion and vision (and of course leadership). You have all the numbers in your pocket. You have strong experience, etc. etc.... now you just need that extra booster... So work HARD to make yourself an original impassioned, fascinating applicant, and you'll have done the best you can.
And one more thing: Start NOW! It takes time and thought and effort, and HBS already released their questions.
Go get 'em killer!
