I think the only reasonable way to achieve the same number of matches is to have 7 rounds of 4 matches and 1 round of 5 matches, with each team playing 6 times. For example:
(2 11) (3 10) ( 4 9) ( 5 8)
(3 1) (4 11) ( 5 10) ( 6 9)
(4 2) (5 1) ( 6 11) ( 7 10)
(5 3) (6 2) ( 7 1) ( 8 11)
(6 4) (7 3) ( 8 2) ( 9 1)
(6 7) (8 9) (10 11) ( 1 2)
(3 4) (5 6) ( 7 8) ( 9 10)
(7 5) (8 4) ( 9 3) (10 2) (11 1)
You might want to consider a swiss guided round robin. Start with a round robin schedule like this:
11 or 12 players
Rd Pairings
1: 1-12 7-6 11-2 8-5 10-3 9-4
2: 12-7 2-1 6-8 3-11 5-9 4-10
3: 2-12 8-7 1-3 9-6 11-4 10-5
4: 12-8 3-2 7-9 4-1 6-10 5-11
5: 3-12 9-8 2-4 10-7 1-5 11-6
6: 12-9 4-3 8-10 5-2 7-11 6-1
7: 4-12 10-9 3-5 11-8 2-6 1-7
8: 12-10 5-4 9-11 6-3 8-1 7-2
9: 5-12 11-10 4-6 1-9 3-7 2-8
10: 12-11 6-5 10-1 7-4 9-2 8-3
11: 6-12 1-11 5-7 2-10 4-8 3-9
and choose rounds that match up as many perfect scores as possible. Any team paired against 12 has a bye that round. Once there is a clear leader, choose unplayed rounds at random.