Check your Commercial Code for something called a "cutoff hour". In CA, we must accept a stop payment until the earlier of the midnight deadline, close of business or the cutoff hour (unless the item was cashed before the stop).
In your example, presentment is "today" and you have until midnight tomorrow to return the item. The cutoff hour can be no earlier than 1 hour after opening, so that is what ours is. Tonight's presentations can be returned for a stop payment until 10:00 tomorrow morning.
That also applies to legal processes received by 10:00. We have presented items returned if necessary for the levy.
Al Miller, CRCM
Opinions expressed are my own and not necessarily shared by my employer.