We have something very similar in Chile. But instead of each party representatives counting votes separately, the person that was responsible for each voting "table", shows each vote to the party representatives (put it in front of him/her like someone showing which card he/him took from the magician 😄), and other person marks the vote on a whiteboard that everyones also sees.
At the end the process takes a similar duration, and TV channels show different voting tables in real time as they publicly count votes.
With these methods is practically impossible to rig elections and the results are very fast. What USians do is nuts, leaving some single entity count votes behind close doors? And those votes aren't even what defines the elected president?