Update to Double Elimination Tournament

As per my understanding, I agree with your table except for row 8. By this description

…after round 7 the condition

… is not met, and so I believe that there are two byes in round 8 - one for the first tier winner, and one for a player from the second tier. So the table would continue like this:

 5                   2                       10
 6                   1                        6
 7                   1                        3
 8                   1                        2
 9                   1                        1

… and then the finale takes place in the tenth round.