I’d tell you what I would have done.
One week won’t make any difference now. It all depends on your class start date, your present job scenario, last deferral date and fee refund date.
A general advice. If they want to give you results by Aug 6th. Then raising GCMS request won’t make much difference. Your BVL is also too late. If your course starts wayyyy into the fall (Sep mid) then wait if you have a fear that it will delay your processing. If time is of essence, raise a GCMS request ASAP. 10$ well spent.
All the best buddy. Hang in there.