You don't want any system that ties a particular vote to an individual. That would be the death of secret ballot. There is a reason for keeping those things separate.
Mainly, if your vote CAN be traced to you, you can be pressured to vote a certain way. Or, you could reliably sell your vote, since you have the means to guarantee what it was.
Nope, the way to stop the fraud is to stop the fraudulent votes from entering the system in the first place. After they get in, you're stuck with them.
I understand your point, but I think a double blind ballet could be devised to void all associated votes. They currently hold ballets that aren't registered, not to mention absentee ballets. You could do this with all of them until the SSNs are compared. However, there is no risk at all in entering your SSN when you vote, thus insuring that the particular SSN only votes once. And it is probably adequate to simply use it for registration, and have a system that cross checks all systems for the dead and duplicates 24 hours before the polls open.