so the top 256 would be in one tournament, the next 256 in another, and so on.
I think 256 is not enough. There are 14 weeks in BB, which means if single elimination is used and there is one game per week, 16384 teams could be in what is now called the B3, 16384 in the 2nd tournament and 16384 in a 3rd tournament. The remaining teams would not make the cut. Qualification would be based on world ranking and how well you did in last season's tournament.
I understand the BBs do not want much happening in the last week of the season, so one or more weeks could have two game played (like the semi-final and final game).
Other possibilities:
-a qualification game towards the end of the season to get into the 3rd tournament.
-the 2nd tournament has an extra game, so 32768 teams participate in it.
Run of the Mill Canadian Manager