I don't know what to tell you. I'm not an adcom, but I certainly wouldn't wait 2 months for one class. What if you hadn't taken it all yet? You'd be fine, right up until matriculation. You could let them know you are retaking it in the "anything else to add" section to address any possible concerns, but the whole world is going to have a boatload of P/F prereqs from last spring, so I just don't see how one class knocks you out of the running.
On the other hand, yeah, submitting before Labor Day also shouldn't be the end of the world, but lots of people didn't receive the COVID love they were expecting last year after submitting later than usual due to what was going on. The very same adcoms who advise that we are all neurotic worry warts had nothing to say other than the usual "seller's market," so, believe me, they don't have all the answers, and every utterance from them is not the gospel.
It's your application, so it's your call. If it were me, I'd submit early and explain I have a single prereq P/F from before I knew I would be applying, and I am presently retaking the class for a grade. If the 3.6/3.5 with an upward trend doesn't knock you out, a single P/F prereq that you are retaking for a grade won't. No matter what your grade turns out to be, A, B or C, it won't make a difference in your GPA or in your outcome, whereas being complete around Labor Day versus mid July very well might.