I have less complicated idea
- classifying the players in 4 groups (A-B-C-D), according your concept of their skills in KaM ( A best, B skilled, C decent, D rookies)
- every player play with every player, 1 match (maybe 2)
- every group have differn points for the win. example: Group A = 4, Group B = 3, Group C = 2, Group D = 1. If A win A it's 4 points, If A win B it's 3 points, If D win A it's 4 points, If A win D it's 1 point and so on... And then we have standings and who win, he get points. Like football.
the league duration is 3-4 months, every player choose with who will play first. At the end, for official place on the standings, every player must to play at least 70-80% of the games. But who play more games should be rewarded with points at the end. When we will have official standings then we announce the winner or we decide to play final 4 (or final 8) like tournament styel where we get the champion.