There is no need to do anything different than this simple counting-by-hand system. Computers, in the form of punch cards, were introduced into US voting systems for reasons of convenience and profit, and not for accuracy. There's nothing more accurate than a double count done by hand, and it doesn't take that long. Ask a veteran pilot how they feel about computers arbitrarily taking over functions in the cockpit.

By prosecutors in cocaine cases, until the first case in which a defense lawyer requested and got, with the judge's permission, the cash out of the prosecutor's wallet, sent it off for testing for cocaine, and came back with a 100% positive test for cocaine traces on every bill. How many people were wrongly convicted with the help of the prosecutor's trick of pointing out "traces of cocaine" on the money in evidence, was exposed?