You can start counting during the election. So, counting the last hundred or so ballets in ~1hour gives plenty of time for accuracy.
That seems very odd. Can you actually do that? Around here the polling location must first ensure that the number of votes cast matches the number of votes recorded during voting, only after that can they open the urns and start tallying.
PS: Saying you need to change the law when that must happen with any significant change anyway is kind of a minor hurdle.