We are going to have to move to a national voter registry at some point.
Tie your voting to your SSN and IRS tax filing.
Claim a primary residence and your vote goes to that state and district so you can't vote in two states.
Provide the ability of a secure web based voting solution to make voting easier for anyone traveling or has work on election day.
Provide some small tax credit as an incentive to vote.
The states can still take ownership of voting places for people that want a place to go to and cast their vote but their system would have to be tied to the national database that could throw out votes of people that have moved or are not legit for any reason.