I am very impressed by the amount of leadership you say you have, and that in of itself is quite exceptional and should make you a potential candidate for Top 10 schools. And I am very curious why you didn't get accepted, or even invited to interviews. I would really love to see your essays, because my gut tells me either you messed something up, or didn't write about the right things in the right way.
You for sure can reapply to some schools, for all schools take reapplicants and the accept rate is about the same as it is for the general population. The KEY though is: what has IMPROVED since your last application. Let's assume you will get better essays and recs in this year... but still some CONCRETE improvement over the last year (like a promotion) will go a long way.
For the GMAT thing, it's complicated always. A 710 is good enough to get you in anywhere. This is the truth. And from there on, it's your profile that is getting you in. Will getting a 730 be better? SURE! And especially for a reapplicant who is obliged to show improvement. But the question is always one of payoff. Your time is limited as is your energy, so what will be more worthwhile? And it depends on so many things, I don't want to give you an easy answer (how good your essays are, how much time you would have to dedicate to it, how much better you might potentially do, how much you are willing to compromise on schools).
But like I said, from here on in, I think the place to start is to review all your applications from last year, and figure out what went wrong and how to make good on that.
Hope this helps!