9/24 is fine. You don't need to submit by 9/21. Just don't submit 9/27 or 9/28 if you can avoid it. The report from previous years is that the site crashes a lot with the uptick in traffic, so best to avoid the last couple of days before the deadline. But I don't think 9/24 will be an issue.
ETA: are you applying derm, gen surg, or IM? If you're doing the supplemental app thing, that's a different story. I'll defer to somebody applying in those specialties if that's the case. But for everybody else, doesn't matter when you submit as long as not last couple of days.