red769:
I imagine most will agree with me here, but the biggest concern is your GMAT score. A 680 is no doubt a respectable score but it's going to make things a little tricky for some of the schools on your list such as LBS, LSE and INSEAD. For someone coming from a competitive demographic such as you, you probably need to get at least a 700. Would you consider retaking the exam prior to applying?
You won't get filtered out outright, but I'm not seeing the "wow" factor in other elements of your background that will strongly outweigh a below-average GMAT score. It might exist, but sometimes it's hard to gather from these posts where you have to summarize (rather than detail.)
In any event, please reach out to us if you want to discuss your background, the GMAT, and your school list in more detail. We offer free consultations to those actively applying.
https://admissionado.com/free-consultation/