At the end of polling day, distribute all uncast votes evenly between the candidates.
A lot of people may not care who gets elected, but the idea of a computer or a bureaucrat getting to use their vote for them would cause such consternation that they’d go along to make sure it didn’t happen.
If the votes were split evenly between all candidates, then it wouldn’t make a difference to the outcome; for the purpose of deposit retention, we could specify that candidates needed to get 5% of the directly cast votes.
You may not like any of the parties, but I bet there’s one you loathe more than the others. Fancy taking, say, a one in six chance that your vote goes to them?
Then again, this idea – like almost all ideas proposed to increase turnout – assumes that voting, rather than being sufficiently engaged to want to vote, is the key thing.