Sorry to hear about last year's results. The key thing when reapplying is to show how you improved in the year between. It seems like you've had some really interesting leadership opportunities professionally in the start-up over the past year, so that should improve your leadership profile. I didn't really see any new extracurricular or community activities of substance -- were there any?
My sense is that your GMAT is not really the issue (am a little surprised by UVA's feedback, in fact). I think the deeper issue lies in the lack of community leadership and post-college extracurricular activities. Since the time you applied, though, I think your professional leadership profile has improved, so this should improve your chances.
I really can't tell you what to do in the end, as there is no 'right' answer. You certainly can retake the GMAT and try to improve your score. If you go this route, I'd suggest you do this sooner rather than later (take the test in August or early Sept). Then you'll know which range of schools to focus your efforts on. You'll still have time to submit at least 1 R1 application and several R2 apps. Alternatively, you could opt not to retake the GMAT at all, and apply to a range of schools, focusing your efforts on the application itself. Either option is viable - just depends on your own personal risk tolerance and your personal goals in terms of schools. I'd recommend against your option #2 below - that is a recipe for very split attention and anxiety (once you start the apps, you get into a groove, and interrupting that with GMAT would be highly stressful/difficult).
If you have two target schools that you like equally, you should apply to both. If you must choose, choose the one you feel is a stronger fit. There is no disadvantage to reapplying, unless you haven't improved your profile at all since you last applied.
4th to 15th doesn't mean too much to me as schools vary a fair amount by different rankings. Given your results last year, though, you might add one safer school (in the 15-25 range) to be safe (if there's one you would go to, that is!)
As I have no indication of what your career goals are or what you are looking for in a school, I would have a hard time suggesting specific schools for you to apply to. Think about what you want, not just where you can get in! Each school is different - do your research on each and you'll start to get a sense for which ones are best for you. Hope that helps!
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