You’re absolutely right. The first thing is to stop the early voting....and absentee voting for anyone.
I agree on getting rid of early voting completely. It's much fairer to have the large majority of votes all cast on the same day and with about same informational environment available to almost all voters at the time of the voting.
But early voting is also an impetus to organized fraud, because the more time the polls are open, the greater the opportunity for cheaters to cast multiple votes.
As for absentee voting, I wouldn't throw it out completely, but tighten up the grounds for allowing it.