See this link for the ISB site:
Taking the GMAT for ISB. They state that they consider applications even on unofficial scores provided the official score reaches in about two weeks.
Theoretically, you could schedule even for Oct 15 and still face no problems in the consideration of your application. We have seen some people take the GMAT on the last day before the deadline in the past and make it. However, would advise you still keep a 4-5 day extra buffer, and plan to take the exam by around the 10th latest.
In case you feel you are still not able to achieve stronger scores, consider pushing your application to Round 2.