The trouble with cheating like that is that it is very easy to prove you wrong. All they have to do is canvass the registered Republicans in those districts, asking them to sign a sworn statement that they voted in a 99% polling station. If they can come up with greater than 1%, then they demand access to the poll registrar, to see if it indicates that they did vote there.
If the registrar does not have their signature, it presents a case that indeed the ballot box was tampered with; if it does, yet more than 1% attest they voted Republican, this also shows that the ballot box was tampered with. In either case, this points the finger squarely at whoever was in charge of ballot box security.
If the box shows no sign of tampering, it goes even further, as it indicates the box was resealed.
There are pretty exact parallels with electronic voting as well. Eventually a person or people are directly implicated in a criminal act. Then, hopefully, enough pressure can be brought to bear on them to confess, rather than go to jail.
No one has the will to pledge their lives, their property and their sacred honor.