Who cares if the source code is public or not? There is never going to be a way to verify that it is running on the machine when you are standing in front of it.
We can't predict all of the problems that come up and that alone tells us we need to be in the best position to anticipate changes, hence respecting software freedom for all computer owners. Therefore not being able to inspect that the running voting machine is running trusted software is no reason to deny any computer own their software freedom. That's no justification for pushing voting districts into buying new voting equipment which ostensibly supports the needed change.
So in the end the solution remains the same: anyone who cares about software freedom (as we all should) would care that their voting machines run on free software.
Paper ballots, electronic tabulation. Can be recounted by hand if necessary.
Or, pencil and paper ballots.