I think having a database of votes tied to individuals is a horrible idea.
Secret ballots are important.
Yep, can't steal elections without them.
I agree entirely that secret ballots are important. That said, the randomly generated alphanumeric codes would NOT identify individuals. They would be randomly generated at the time you receive the ballot, seen by no one but you, and you would write the code on the ballot and on a piece of paper only you would have. It could not be traced to you. The only purpose would be for you to be able to verify that the vote counted for that alphanumeric code was the vote you cast.
Another way to do it would be to require people to vote twice, once into the machines that would be counted as usual, and the other would be into a separate machine/ballot box that would be counted separately (by different people). If the vote totals between the two didn't add up, it would raise a red flag.