Regarding your application, 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 your position, admissions teams are always looking for candidates with leadership and management experiences, and if this will provide that it could be a good opportunity. I recommend you pursue the position though because you feel it is the right fit for you, as opposed to only selecting the job because of how it would look to an admissions teams.
For your application, I recommend aiming for at least a 700 on the GMAT exam. I do not know enough about your background, but extracurricular activities will also be looked at on your application, and provide a good opportunity to showcase leadership experience.
Here is some school specific advice for the programs you are considering:
INSEAD: http://www.stacyblackman.com/business-s ... ub/insead/
LBS: http://www.stacyblackman.com/business-s ... ss-school/
Conrad and the Stacy Blackman
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Stacy Blackman | Stacy Blackman Consulting Inc | http://www.StacyBlackman.com | +1 323.934.3936
MBA blogger, US News and Author, The MBA Application Roadmap