Hi mtouchton,
GMAC has publicly stated that the Official Score that you earn on Test Day is within +/- 30 points of actual ability. Your 2 Official Scores (580 and 610) are close-enough to one another that it's unclear whether you'd actually receive the 'benefit' (from showing both scores) that you're interested in. You're ultimately asking Admissions questions, so you would likely find it beneficial to speak with an Admissions Expert about your overall profile. Those Experts should be able to answer your Admissions questions and help define the specific areas of your profile that could use some improvement.
There's a Forum full of those Experts here:
https://gmatclub.com/forum/ask-admissio ... tants-124/Assuming that you're still studying for the GMAT, before I can offer you any additional advice for your studies, it would help if you could provide a bit more information on how you've been studying and your goals:
Studies:
1) On what dates did you take your 2 Official GMATs?
2) How long did you study before each of your Official GMATs? Right now, how many hours do you typically study each week?
3) What study materials have you used over the course of all of your studies?
4) On what dates did you take EACH of your CATs/mocks and how did you score on EACH (including the Quant and Verbal Scaled Scores for EACH)?
Goals:
5) What is your overall goal score?
6) When are you planning to apply to Business School and what Schools are you planning to apply to?
GMAT assassins aren't born, they're made,
Rich