Many countries around the world have proven that paper and pencil voting is reliable, traceable, and scalable. Even in countries with mandatory voting where the turnout density is higher than the US.
In Australia, most public schools & town halls become voting centers for the day, so most people don't have to travel far and the numbers are manageable. A small army of trained electoral commission recruits control the process, and do the counts at the end of the day. The results are in that evening, which is plenty fast enough.
Paper voting has several distinct advantages:
1) It has a visible and tangible chain of trust, and can be directly inspected by the lay-person.
2) It directly involves people in the democratic process, not machines
3) A lot of the money required to run the election goes to individuals, not corporations.