Here's an idea on determining winner after 4 days.
At the start of a round, I'll ask players to "check in" by posting in the tournament thread. Basically, confirm that they've seen the bracket and that they'll actively try and work out a time with their opponent.
If the 4 day limit hits, and only 1 of the players in the matchup has checked in, the player that checked in is declared the winner. If both or neither player checks in, winner is determined by coin toss. You also can't win by default twice in this manner. Example: In second round, a match doesn't happen. One player won a game by default, other player won a game fair and square. Player that played a game before is declared winner.