Every mail vote collected by the Postal Service gets delivered on the election day to the assigned precinct. At the end of the day, all those votes are mixed in the ballot box and then counting starts. It takes no more than three hours to get the 99.5% of the votes counted nationwide.
In order to vote by mail, you have to walk into any Postal Service office with your valid government ID and explicitly ask for it. The PS agent will verify your identity and will send you the voting papers to the address you register into. Then, you do your choices and go back to any PS office and send the vote to your electoral precinct by certified mail.
From the moment you ask for mail voting, you get marked in your precinct as a mail voter, so you cannot go in person and vote anymore. You can, though, on the election day go to your precinct and verify that your vote is there.
I don't see the difficulty on this.