Mid September puts you at a significant disadvantage, even if you have a strong application.
By the time you are offered an interview, there may be nothing left but waitlist decisions.
This timeline will vary depending on the state of residence. In other words, the timing is more important in very competitive states (e.g. CA) and less important in others.
If your application is more modest (and there is no way of knowing without an MCAT score!), it would be very late indeed.
That said, do not risk a lower score by taking the test sooner if you need more time. All MCAT scores remain a part of your application forever and despite what a school may say about how multiple scores are interpreted, no one can predict how any individual screener may view them. They can't be "unseen."