Duke,
I think you have too many constraints to get a good solution, or at least I don't know how to find a good solution with this many constraints. The schedule below will at least make sure that everybody gets to play all games once, however the pairwise balance, or social mix within the foursomes, is compromised in order to achieve this.
Below I have used "R" to represent the rounds, "G" for the 9 type of game and 1 to 36 for the players.
Hope that helps,
Ian.
R1 G1 (17 32 26 2)
R1 G2 (24 3 11 28)
R1 G3 (31 14 5 21)
R1 G4 (20 8 35 10)
R1 G5 (27 18 36 4)
R1 G6 (12 7 25 34)
R1 G7 (9 29 16 22)
R1 G8 (13 33 1 19)
R1 G9 (23 15 30 6)
R2 G1 (18 33 27 3)
R2 G2 (25 4 12 29)
R2 G3 (32 15 6 22)
R2 G4 (21 9 36 11)
R2 G5 (19 10 28 5)
R2 G6 (13 8 26 35)
R2 G7 (1 30 17 23)
R2 G8 (14 34 2 20)
R2 G9 (24 16 31 7)
R3 G1 (10 34 19 4)
R3 G2 (26 5 13 30)
R3 G3 (33 16 7 23)
R3 G4 (22 1 28 12)
R3 G5 (20 11 29 6)
R3 G6 (14 9 27 36)
R3 G7 (2 31 18 24)
R3 G8 (15 35 3 21)
R3 G9 (25 17 32 8)
R4 G1 (11 35 20 5)
R4 G2 (27 6 14 31)
R4 G3 (34 17 8 24)
R4 G4 (23 2 29 13)
R4 G5 (21 12 30 7)
R4 G6 (15 1 19 28)
R4 G7 (3 32 10 25)
R4 G8 (16 36 4 22)
R4 G9 (26 18 33 9)
R5 G1 (12 36 21 6)
R5 G2 (19 7 15 32)
R5 G3 (35 18 9 25)
R5 G4 (24 3 30 14)
R5 G5 (22 13 31 8)
R5 G6 (16 2 20 29)
R5 G7 (4 33 11 26)
R5 G8 (17 28 5 23)
R5 G9 (27 10 34 1)
R6 G1 (13 28 22 7)
R6 G2 (20 8 16 33)
R6 G3 (36 10 1 26)
R6 G4 (25 4 31 15)
R6 G5 (23 14 32 9)
R6 G6 (17 3 21 30)
R6 G7 (5 34 12 27)
R6 G8 (18 29 6 24)
R6 G9 (19 11 35 2)
R7 G1 (14 29 23 8)
R7 G2 (21 9 17 34)
R7 G3 (28 11 2 27)
R7 G4 (26 5 32 16)
R7 G5 (24 15 33 1)
R7 G6 (18 4 22 31)
R7 G7 (6 35 13 19)
R7 G8 (10 30 7 25)
R7 G9 (20 12 36 3)
R8 G1 (15 30 24 9)
R8 G2 (22 1 18 35)
R8 G3 (29 12 3 19)
R8 G4 (27 6 33 17)
R8 G5 (25 16 34 2)
R8 G6 (10 5 23 32)
R8 G7 (7 36 14 20)
R8 G8 (11 31 8 26)
R8 G9 (21 13 28 4)
R9 G1 (16 31 25 1)
R9 G2 (23 2 10 36)
R9 G3 (30 13 4 20)
R9 G4 (19 7 34 18)
R9 G5 (26 17 35 3)
R9 G6 (11 6 24 33)
R9 G7 (8 28 15 21)
R9 G8 (12 32 9 27)
R9 G9 (22 14 29 5)
