Even if a hypothetical voting machine was open source, and developed by an independent 3rd party, it's still not enough IMO.
How many people in the country can correctly audit complicated cryptographic protocols? How many can fully audit a codebase like this? And how many of those do you think would instantly shut up if threatened with a lifetime of jail or death?
Have you ever seen the underhanded C contest? It's nearly impossible for seasoned developers to find the problems with some of those, in a contest where they KNOW for a fact that there is an exploit, and even sometimes what that exploit is trying to achieve.
I can make a complete guess at the number of people capable of auditing this in the US being less than 1000, and the number of people in that position willing to sacrifice everything to tell the world about their discoveries being basically zero.
But let's even ignore that, let's say that there are tens of thousands of capable engineers chomping at the bit to review this. How do you prove that code is what is running on your voting machine? How do you know the hardware is secure? If you come up with steps to fullproof verify, how many people will check it? How many people will be capable of checking their cryptographic proof (if the scheme has one).
This is voting, 1-2% can make all the difference, and if a bad actor can modify 1-2% in some key areas, they can swing the whole election.
Stick with paper checkmarks thrown into a ballot box, written on with pencils. Then every single person that is able to count can help "verify", they can guard that box all election day if they want, 1 or 100's of people can all do it, old, young, english speaking or otherwise.
We have a nearly perfect system right now, but nobody wants to use it, and I can't for the life of me see why.