Formula fields: set re-calculate run time

On a formula field (Sum, Count, Max, Min), I'd like to be able to set the time that this field re-calculates so that I can ensure that the field gets reset at the appropriate time within my workflow.

Use Case: Currently I have a count field that includes a "Date is today" filter. Since the field happens to process daily at just after midnight in my app's timezone setting. But, I actually need to re-run this formula after the night shift has ended from our overnight nursing shift which is at 7am. My "Date is today" filter is only accurate before that time, but not all of the records have been entered at that time.