I can find solutions for two of your schedules by using software for generating experimental designs (for example there are similarities here to a crop experiment where different varieties are planted out in a grid pattern). I haven't manged to find a good solution for the 12 player schedule.
9 players:
2 8 9
6 5 1
7 4 3
4 9 7
3 6 2
5 8 1
1 7 3
9 2 5
8 6 4
2 1 4
6 7 8
9 3 5
5 4 8
1 2 7
3 9 6
7 5 6
4 1 9
8 3 2
15 players:
7 8 10
6 13 2
11 15 14
9 5 1
12 4 3
14 10 4
6 8 5
13 11 9
2 12 15
3 1 7
8 9 2
15 10 6
3 14 13
1 12 11
5 4 7
13 7 15
4 2 1
5 11 10
9 3 6
12 14 8
4 15 9
11 3 8
7 6 12
10 1 13
14 2 5
10 9 12
8 13 4
2 7 11
15 5 3
1 6 14