As you stated, the earlier the better. 2 months isn't going to make much of difference in my honest opinion. If you think you are a below average applicant, it is probably better the interview early. If you are a competitive applicant, you're probably good to apply probably anytime before 2 months before their deadline.
So it really depends, but I think you'll be fine applying in September. I applied in December and mid-March and still got interviews at all the schools I applied.