Um... Even if there were NO machines, how difficult would this really be? At each precinct, poll workers tabulate votes, under the eyes of poll watchers. They send the ballots to a central location for safekeeping under lock and key, call the main office to report totals, and go home.
It would take one person a long time to count a million ballots. Or 100 million. But it wouldn't take that long for a group of people -- poll workers and poll watchers -- to count a thousand ballots, and very little time to total their totals.
And we'd have a election process we could trust.
Am I missing something here?