Hi there,
Congrats on your score improvement! I would say in general if you score a 680, yes with additional prep a 700+ could be in reach, especially if you've scored that on practice tests that are also adaptive. Keep in mind that the GMAT has a margin of error too, and technically your score on a given day could range +/- 20-30 points or so. You could even try again in one month with another 1-3 full practice tests and review, and a quick last-min study push, if it were possible, as opposed to investing another full 2 months to the point that it becomes counter productive or you get tired of studying.
Schools will take the highest score, and taking it 3 times will not a be a problem. Not sure what your math/verbal breakdown was as that is also relevant. Being sure that you have a strong quant score can be particularly important given the quantitative nature of business school, and the fact that your GPA is below average means the GMAT can help balance that out to a certain degree.
You do also have fewer years of work experience than average, though you mentioned having great quality experience in work and in life which is a plus. But given the fact that you have worked less time and have a lower GPA, yes getting 700+ would help at the top-ranked schools. No matter what Stanford will be a 'reach' school as it is the most competitive program out there (high GMAT scores and huge number of applicants for a smaller-than-average class size). Kellogg and UCLA and Darden would still not be easy but better odds than Stanford. You'll also need a strong reason why getting the MBA NOW (vs working another year or more) makes sense for you, based on your goals, to have a chance at acceptance.
I know that is a lot to think about on many levels; hopefully that helped in some way. In summary I wouldn't say it's mandatory to re-take, but you do have some potential weaknesses in your application so a stronger score could be useful and no matter what you'll have some explaining to do about why go NOW as opposed to later. ;)
Best,
Jennifer Kedrowski
MBA Admissions Consultant
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