If a guy contacts you through P411 about a future date, and the two of you go back & forth through regular email (outside of P411) to finalize a time that works, should the guy go back and send an updated appointment request through P411?

I have, but it feels redundant and rarely has the provider bothered to respond to the P411 reschedule email.  We just meet up as we'd agreed through the regular emails.

If you are communicating through email there should be no reason to go back to P411. It may even be confusing enough that she doesn't realize it's the same person, stick with the same method of communication rather than jumping back and forth.

Whether you send me a pre-screening request, and appointment request, or a pm, once I have someone's p411 information confirmed, that's all I need.  
Then after the appointment, go back and send an okay request.