It's very clever, but not as useful as it seems, and impractical as it does not adequately allow for human nature. If people are told to make two marks to vote for someone and one to vote against them, many will put one mark on the first ballot paper against every candidate, put a mark on the second paper for the candidate they wish ot vote for, and leave the third blank. Then the second ballot is simply the plain ballot that would be used for normal ballots and the other two contain no information.
Secondly, the protection provided by being able to check that one ballot has been counted is reliant on you randomly picking which ballot to copy. People are very bad at this, so it may be possible to miscount ballots which are known not to have been copied.
And when someone finds their ballot wasn't counted, what do they do about it? And how does this differ from what someone would do if they fraudulently wanted to claim miscounting? What stops someone adding an extra mark on their copy?
Anyway, it seems that the scheme is solving the wrong problem - it is trying to provide a means to detect miscounting when what is really needed is a means to prevent miscounting. We can already solve the latter - have lots of people involved in manual counting so that it is impractical to corrupt enough of them to make a difference to the result.