Nathan,
I think it may be impossible to come up with something reasonable as the scenarios you are considering are asymmetric. For example think about forming teams of 3 when there are 3 women and 6 men. Any man has a pool of 8 possible players they can play WITH, but the women have a pool of only 6 possible players.
So my suggestion is to modify the format slightly to introduce the missing symmetry. Consider dividing your 9 players into 3 groups, 1 to 3, 4 to 6, and 7 to 9. Now the extra condition on the tournament is that all teams of 3 players must consist of exactly one player from each group. This solves the problem mentioned above, since now everybody has exactly 6 possible team partners, and they can have a tournament along the lines you suggest where each player:
(1) has 6 games and 3 byes
(2) plays WITH the 6 players from the other two groups exactly twice.
(3) plays AGAINST the 6 players from the other two groups exactly twice.
(4) plays AGAINST the 2 other players from their own group exactly three times.
Here is an example of a schedule that meets the conditions above:
round on court sit out
1 (1 4 7 v 2 5 9) (3 6 8)
2 (2 5 8 v 3 6 7) (1 4 9)
3 (3 6 9 v 1 4 8) (2 5 7)
4 (8 1 6 v 7 2 4) (3 5 9)
5 (9 2 4 v 8 3 5) (1 6 7)
6 (7 3 5 v 9 1 6) (2 4 8)
7 (5 7 1 v 4 8 3) (2 6 9)
8 (6 8 2 v 5 9 1) (3 4 7)
9 (4 9 3 v 6 7 2) (1 5 8)
I think you would use this schedule by assigning one group to be women, one group to be 3 highest ability men, and the third group to be the 3 lower ability men.
There are exactly 360 ways of making the schedule above, where all the teams of 3 are different and all 9 games are different! Send me an email if you would like to see the alternatives.
Hope that helps,
Ian.
