Hi randompigeon,
First off, a 710/Q44 is an outstanding overall Score, so you can comfortably apply to any Business Schools that interest you. The Q44 won't "impress" anyone, but it won't necessarily keep you from earning an invite either (with the possible exception of highly-competitive Finance or Specialty Programs). You're ultimately asking Admissions questions though, so you would likely find it beneficial to speak with an Admissions Expert about your overall profile and plans. 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/
If you do choose to retest though, then we have to examine how you were studying for the Quant section before. Once you've decided on whether to retest or not, you should post back here (or you can PM me directly) and we can talk through your study options going forward.
760+: What GMAT Assassins Do To Score at the Highest LevelsGMAT assassins aren't born, they're made,
Rich