Making election day a holiday probably won't have the effect you're hoping for.
Best case: Almost everybody goes to work as usual. A few of them get a pay differential for working the holiday.
Worst case: Holiday means holiday. We'll give all bus drivers the day off to vote -- and hope the bus riders live within walking distance of their polling location.
It's already illegal to open other people's mail. Intercepting mail in the US is a really quick way to get absolutely fucked by the law. There haven't been any cases of people's votes being recorded as far as I've searched. What more would you want?
An online voting system would be great. Keep the in person, just allow online as well, election locations all the sudden are not busy at all and online is easy access.