> Because having groups of random, untrained people squinting at dangling chads is less error-prone?

What on earth? I marked the candidate I wanted to vote for with an X in a circle on a paper ballot. Marking circles for more than one candidate is a spoiled ballot you can replace instead of depositing if you wish. This isn't rocket science.

Computer-based systems that print out a machine-readable paper ballot that can be hand-counted as well. You vote (perhaps with a touch screen, perhaps not) by making your selections, printing out your ballot, examining it, and inserting it into the tabulator once printed.

There's still plenty of margin for error (for instance, the printer could run misprint or run out of ink, the tabulator could be buggy), and corruption ("here, let me file that for you...") but I think it maximizes the benefits of touchscreen voting for disabled voters while minimizing the downsides.

Normal(paper) vote with one reviewer per political party.