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.