It's so comical watching a country that claims to be first world struggling with this.
My shit country has solved this _ages_ ago:
Every citizen has an id.
The IDs are issued by each state, but they are all functionally the same. You will have no trouble voting with an out-of-state ID.
That ID is free and relatively easy to get.
Every citizen has an assigned place (building, room and ballot box) to vote, and it's usually close to their residence (you are expected to update when you move, it's also very easy).
Each ballot holds no more than 600 votes, average is around 300. Lines are uncommon, it usually took me like 5 minutes to vote.
Voting takes place on a Sunday, and most cities make public transit free of charge.