If you are applying to mostly MSTP programs, make sure that you check the deadlines of the schools you are applying to. The earliest deadlines I know of are Sept. 15th, but even schools with deadlines in early to mid October may be problematic for you if your primary isn't even verified until sometime in September.
From my own experience, I can tell you that unless you are the best applicant ever, being complete too close to the deadline (less than one month), is like shooting yourself in the foot - you'll probably have a nice "we ran out of interview spots" letter a week or two after finishing the secondary. You should be fine submitting in August, but you may want to cut out any schools with early deadlines.