Reality is messy. This same imprecision in getting the clock stopped exists at every clock stoppage the entire game. Our solution to the problem is classically human. We ignore it completely and pretend it doesn't exist. Except on those rare occasions when it is noticeable, and critical enough to somebody that they complain. Then, and only then, do we address it with a rule about what to do to fix just that one little part of the problem.
So in your DA case, Camron, I humbly suggest that unless the problem is noticeable, that it simply be ignored.