Photo ID is the only thing that will work.
Fraud goes on predominantly in areas that are heavily democrat. This system would effectively eliminate it at the presidential level, but you are correct, voter id would be necessary to combat fraud in statewide races.
Photo ID may help a little, but professional voter fraud is enacted by those who work inside the polls. One poll worker can simply vote as many times as needed. Second, even if you have a photo ID, they would simply go up and down through town and vote at each poll. Do you think they bother to get a bus load of people to go to one poll and vote only once? Rules only matter if those in the polls enforce the rules. WI has same day voter registration, so when they bused in from MI to knock off the state senator in the recall election, do you really think they went through all that hassle to only vote once. Voter ID is a feel good start, but would do little to stop fraud