Can I choose when payment reminders go out?

Yes. Reminders are scheduled as day offsets around the due date, and the school sets the list itself — by default seven days before, three days before, on the due date, three days after, and seven days after.

Any offset you do not want is simply removed from the list, including all of them if the school prefers to chase payments its own way. One invoice receives one reminder per offset, however often the daily check runs.