Thanks for posting.
Regarding your first question, nothing about your story makes me think there is any reason why you cannot be admitted, but nothing stands out telling me why you should be admitted. All of the reasons why a top program would admit you are in the details of your work experience, personal experiences, personality, values and overall story.
For which round to apply to, you should apply when you feel your application is strongest. Ideally this will be in the first round. One thing you should avoid is applying in the final round.
If you believe you can improve your score by 30+ points, then there isn't any harm in taking the test again. Your highest score is self-reported on your application, so admissions teams will focus on your best score.
Here is some school specific advice for the programs you are considering:
Kellogg: http://www.stacyblackman.com/business-s ... n-kellogg/
Booth: http://www.stacyblackman.com/business-s ... ago-booth/
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