They either need to have 5 wild-card teams per league, so there's 8 teams and everyone plays a first round series, so no one has to wait for the first round to finish (which would be completely ridiculous) or they need to make the wild-card round a best of 3 series, 3 consecutive nights all in the city of the team with the best record. That would minimize wait time for the other teams, but still ensure that the better team advances most of the time.

As it is now, the wildcard "round" is like the first 4 games in the NCAA basketball tournament. They mean something to the teams involved, but are ignored by most everyone else.