[EdHominem]

The key to the system you describe is having the vote-punching machine right next to the vote-checking machine. That way if there's a hanging-chads issue you can catch it before it spoils more than a single vote. And the person just slides the vote down the 'discard' chute and gets a fresh one until they're happy with the results.

Have the checker mark the holes it detects with red ink or something, to make it clear to the user that the system detects their votes properly, and to provide a fallback. In the event another machine fails to count it, the user's intent is double-marked.

And then have the same style of vote-counting, where people manually scrutinize the votes, and have each party's representatives slide the votes into their counting machine. If the machines lose sync, you stop and figure it out at the point of the specific vote that fails to scan.