“sent to the voter’s residence confirming both a vote, and confirming who they voted for”
That wouldn’t be secret balloting.
I thought of that, but was too lazy to explain my work around on that.
What if *one* "sample ballot" was printed for every voter, and each ballot is one of 10-100 or more *different* potential combinations of ballots--the only difference being random spacing/location of the fill-in circles/punches on the voters' particular ballot? The voter's particular combination is given to them after they leave the booth, on a sheet of paper, and their ballot has a specific "voter id" number assigned to it.
When the count is over, the rolls are run again through the machine, and the voter gets mailed a printed punched-paper "receipt" with their designated random "voter id" number instead of their name on the receipt. They put the "receipt" on top of the sheet they are given on election day, and they should match up.