Thanks for reaching out.
Wow, this is a tough one. You are so close with the score you have - 700+ would really take you to that next level. I do think you can clean up, especially with proper applications and thematic setup, but if you think you can get those extra points, it might be worth pursuing.
As for your specific questions:
1. Is it worth retaking the test? Should time and efforts be focused on the rest of the application instead?
If it is zero sum, I would say focus on the applications. You are young enough, interesting enough, and otherwise qualified enough to take a real run with great applications (I would strongly advise using a vetted consultant - call us, all competitors, land a great resource). Worst case, you can always reload for next year with a higher GMAT. But if you think you can do both (another argument for consultant, incidentally, as an advisor can help a great deal with time management and cutting down on the total hours - see how we pitch our services at every turn? Promise that was not intended), you should take another run at it.
2. Will adcomm’s assign any value to an improvement of 680 to 700-720 area?
Not for the improvement in and of itself, but 700-720 behaves differently and falls in a different bracket when being considered. 600-640 or so is in real rough territory. 640-690 is "man, which it was higher but I'll keep reading," 700-730 is a check in the box, 740+ is "check plus." It can make a big difference to move one spot over to that check mark. It takes the GMAT out of the equation and prevents it from being an issue.
3. Will adcomm’s negatively view the GMAT retake since 680 is already within the 80% range of the school’s scores?
No, I can't imagine that would ever happen.
4. Risk and impact of overall lower score and lower quant score during the retake given the usual emphasis on quant scores and 31-day waiting period until the retake
No risk in a lower score on the second test. They only look at the highest.
5. Do I apply with my current score and, if it doesn’t go well this year, retake the GMAT and reapply next year?
See above - yes, this is certainly an option.
6. General view on my candidacy
I like it a lot. Are you open to other schools? With some insight into your career goals, I can make some other recommendations.
Hope this helps! PM me if you want to get into it more, set up a consultation, etc.
Respectfully,
Paul Lanzillotti