lilyfraic:
Based on your description of this opportunity, (which I realize is ambiguous by design), I would take the seat at the M7 school.
Is it safe to assume you applied to GSB and HBS particularly since the former is your dream school? If so, I don't see this job drastically improving your odds of getting in as a reapplicant.
If you turn down this M7 after putting a deposit, you may be blacklisted from that school. They will tell you otherwise but I would definitely not count on being re-accepted after withdrawing.
Harvard and Stanford are fantastic programs but, in truth, all the M7 schools are all fantastic and will provide you with many opportunities to do well in your career. Take the opportunity and move forward in your career.
Congrats and good luck!
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Admissionado