You know, while there's still time to change your mind, you should really reconsider the structure of this thing. The way you have it set up, it appears that it's going to be a round-robin, where one team from each league plays one team from each other league at random. But depending on matchups, seeding could really change the outcomes. If the weakest team from S5 plays the strongest from S7, S7 gets one win. But the other 3 teams from S5 might win, even though if you matched best-to-best S7 would win across the board. One way to "fix" this would be to have the score determined by total PF - total PA, and ignore win-loss. The problem there is that one blowout could change the whole thing (say 3 teams from S1 win 3-0, and 1 team loses 0-70, that would be a huge loss for S1 (-61 PD), even though they won 3 games).
Another option would be to have each league decide seeding before the tourney starts. And then the teams play 1-4 against another league, and the winning
league advances, single elimination tournament style. So if 3-4 teams from one league wins, that whole league advances. And if it goes 2-2, there's some sort of tiebreaker, like total PF-PA across all games or something.
Or you could advance individual teams. You could use a system like this:
http://www.bracketmaker.com/tmenu.cfm?tid=361313 where you basically sort the teams from each league in order of toughness (A-D) and then put them in the bracket and let it go like a standard tournament. But there's not much point in that sort of tournament, because it essentially duplicates the Silver tourney with a minor restriction that each league enter 4 teams.