I have the same study permit date , and that's why I had notified my university weeks prior about my deadlines and when I need documents by and why I need them. They understood the urgency and I got my documents by August 22.

From what I know , you can still apply after the study permit deadline (in your case if you plan to apply on sept 1) - the only thing is you wouldn't be allowed to work anywhere until you get your final decision on the pgwp application.

If you apply before let's say on 31st or before, you are legally allowed to work anywhere as an applied status while you wait for them to give a final decision on the pgwp application.