These Bracket games are fun and interesting. Some recommendations and ideas:
1. Once everyone has completed their round (or even once you know a player will advance), allow the players to begin playing the next round. Do not change the end time to complete the next round, but just allow the player(s) to play the next round when it is determined they have advanced to the next round.
2. Also create some tier specific or multiple tier (ex. Master & TM) specific brackets.
3. Also level specific and/or scoring average specific brackets, such as anyone with a level less than 90, or anyone with a scoring average greater than 60.
4. If you can figure out your opponents score before playing, then just post it in the bracket. Strategy can be to post early or wait to see what score is required to win. This could provide a different type of pressure. Or hide scores from everyone. Don't really have a preference, but either way has different challenges.