I understand how your vote was counted needs to be kept secret from everyone else: the police, your employer, political parties, your lover. Everyone.
How your vote is counted does not need to be kept secret from you, though.
A random voter number could be generated when you vote--and it is only given to you, if you want it. You could go online to check how that voter number was counted after the election. If your ballot was counted wrong, you would have the _option_ of reporting it. You can audit your ballot.
Separately, each ballot could be posted by some reasonable division (such as precinct). The HTML could be selected and entered into a spreadsheet (Excel does this well). Then other people could audit the reported results.