Sumerian:

I think what you are saying is essentially correct.

There is a way to extend this though without requiring the 'leader' to have finished all of his/her games.

IF, at any point in the tournament, a person in the section has a lead such that:

If he loses all of his remaining games (which can be 0 in the case that he is finished) and if any other player wins all of his remaining games, and the player hypothetically losing all games left to play still has a higher point total than everyone else, then it is possible to include that player in the next round.

The easy way to do this programmatically:

1. For each player, 1 at a time, give them a "0" for all remaining games in a section. Call this "worst score possible" (wsp)
2. Add up this point total for each player.
3. For every player other than the one being considered for the wsp, given them a "1" for each remaining game. call this the "best score possible" (bsp) for the remaining players.
4. since you are computing many bsp scores for each single wsp score, if you find one bsp > wsp you can stop the bsp computation loop, and compute a wsp for another player.
5. Once you are done, if there exists one wsp that beats EVERY bsp, then that player can advance to the next round.
6. Once every section has a wsp candidate "seeded", then the next round can begin.

I guess the question becomes, do you want the next round to start as soon as possible, or have some "take a breather" time delay (like maybe a few days)?