In my opinion, if you're managing 680 in MGMAT, dedicated 1 month effort can push you to 720 to 730 on the actual GMAT that will be a huge bonus to the places you are thinking of applying. In your position I would retake it on August 1st.

NOTE:
--> You have nothing to lose unless you get a worse score. So make sure you are certain you can safely manage a 650 again.
--> The advantage of getting 720 or 730 is simply to assure that your application will not be rejected on the basis of your score alone. That's all - you're work exp, academics and extra curriculars will be all that matters once this initial hurdle is passed. 650 is not an app-breaker in my opinion but it is certainly not a strength.

In my case, I know that I will need a good GMAT score as a strength, so I know I need a 720+ score. If you think your application is well-rounded and your work experience is rich enough and filled with enough leadership initiatives, a 650 is a competitive score.

Good luck!