You are conflating a few different concepts. One involves what is "late"? Another is what is "rolling"? And the third is what is "competitive"?
This year, with COVID and delayed MCATs, middle of September is probably not going to be late, although traditionally Labor Day is considered "on time."
Conventional wisdom about competitive is that even a really good application will not be ignored or rejected even if it is "late" so long as it is before the deadline. I.e., if Harvard's deadline is 11/15, they are not going to ignore a 4.0/525 applicant submitting at the end of October, although most people would still argue, due to the nature of rolling IIs (as opposed to rolling admissions, which Harvard doesn't do), you're always better off submitting early, since that exposes you to the maximum opportunity to be called for an II, even though some are always held back until the end.
Yield protection is lower tier schools screening out high stat applicants because they realize they are only being used as safeties, and don't want to waste precious interview resources on candidates unlikely to matriculate. Throwing in more applications now to schools where you are overqualified, because you are worried about being late at the schools you are really interested in, sounds like prime conditions to be yield protected.
If you are worried, find more schools where you are a good match. You're nervous because you see people having some success and you are not participating. But, it's not your fault, because you haven't even submitted yet! .
By the way, you are misusing the term "verified." It related to AMCAS verifying your transcript, not schools receiving your MCAT score. Have you submitted anything yet? Are you actually verified? The answer to that question will make all the difference as to where you stand right now!!!