Very simple solution to the problem:

When you vote, you get a piece of paper saying your name, your vote, voter-id, and the machine's salt.

Whenever a vote is counted, it is added to a public website of HASHES. Thus anybody can verify the totals.

If anybody's recorded vote on the website (taken by hashing their info) doesn't match their receipt, fraud is caught (thus removing votes or changing votes isn't possible). Also, if I didn't vote or am dead, and my info is entered, we can verify no tally appears for my hash.

If the hashes don't match up with all the registered voters via registration forms, then votes have been added. Thus in order to add fake votes, fake voter registration forms must be filled out manually [leaving a paper trail to catch the perpetrator].