If a good half of what you allege is true, then the solution is not “recount”. It makes no sense to use a flawed system that you know you must recount afterwards; it makes sense to use a system which is not flawed.
How about using the machines for the local races and initiatives, but for the president, senate and house reps, you use a system like THIS:
So, now you have something that’s easy to OCR count, but also to eyeball count. And also easy to determine if you have an illegal voter or not.
This is just a thought. But if the problem is as big as you say it is, solve it on the input side, not the output side.