Similarly to Jeff’s proposal I suggest that Sunday of nationals should be two separate brackets. However I think we should do it like world cup groupings for soccer.
Teams from each region are randomly split into 4 groups, the teams in each group all play each other and the top two move onto the championship bracket Sunday while the rest compete in the secondary bracket. That way every single game would matter, every team has a chance to play for the title, and teams would be able to play more even competition throughout the weekend.