Perhaps sort games by adjusted remaining time. Denote by T the remaining time on the clock.
- For Fischer or Japane byo-yomi: adjusted time = T
- For Canadian byo-yomi: adjusted time = T / (number of moves to be played until the end of the period)
- For absolute: adjusted time = T / max((N*0.75-n)/2 ; 10) where n is the current move number and N is the number of intersections on the board.
I.e., when you use absolute time, the system assumes that the number of stones that are played in the game is equal to 75% of the number of intersections until move N*0.75, and afterwards it assumes you have 10 moves left.