Your visa is directly tied to you maintaining studies.
F-1 Grace Periods. An F-1 student may be admitted into the United Status up to 30 days before the program start date listed on Form I-20. An F-1 student may remain in the United States for up to 60 days beyond: the completion of the program of study.
You have 60 days to change the school which will give you a new I20. You then will have some leway on the start time of your next course.
Best path i think you should do is. July 1st week-transfer sevis to Kaplan that offers i20 for SAT/GMAT. Try and choose class that will start in another month or so ( i think once you get a kaplan i20 you can wait for upto 60 days again to start- id verify this.
Start Kaplan, In the mean time apply for MBA school or any masters school. Once accepted get the masters I20. Wait another 2 months to start school. That way you could push it to start if next year.
Of course you could just go back and then start the process again.