I think I would start with this schedule for 6 courts:
[(M01 F02):(M05 F07)] [(M07 F08):(M12 F10)] [(M08 F05):(M03 F06)] [(M06 F01):(M11 F12)] [(M04 F09):(M09 F04)] [(M02 F11):(M10 F03)]
[(M12 F12):(M03 F03)] [(M10 F08):(M09 F07)] [(M02 F04):(M07 F11)] [(M01 F06):(M11 F09)] [(M06 F10):(M05 F02)] [(M04 F05):(M08 F01)]
[(M10 F04):(M06 F08)] [(M11 F11):(M05 F05)] [(M04 F02):(M07 F12)] [(M09 F06):(M12 F01)] [(M01 F07):(M08 F03)] [(M02 F09):(M03 F10)]
[(M02 F07):(M09 F05)] [(M04 F06):(M03 F02)] [(M10 F01):(M01 F10)] [(M06 F09):(M12 F11)] [(M11 F08):(M07 F03)] [(M08 F12):(M05 F04)]
[(M12 F03):(M03 F12)] [(M02 F06):(M01 F04)] [(M06 F05):(M09 F08)] [(M04 F07):(M05 F10)] [(M08 F11):(M07 F01)] [(M10 F09):(M11 F02)]
[(M09 F01):(M07 F02)] [(M11 F05):(M05 F11)] [(M06 F03):(M08 F09)] [(M10 F07):(M03 F04)] [(M02 F10):(M12 F06)] [(M04 F12):(M01 F08)]
[(M10 F11):(M08 F06)] [(M06 F02):(M01 F03)] [(M02 F12):(M11 F07)] [(M07 F10):(M03 F05)] [(M04 F04):(M09 F09)] [(M05 F01):(M12 F08)]
[(M04 F10):(M06 F11)] [(M10 F12):(M07 F09)] [(M09 F03):(M05 F06)] [(M02 F08):(M08 F02)] [(M11 F01):(M03 F07)] [(M01 F05):(M12 F04)]
[(M01 F09):(M07 F05)] [(M06 F04):(M03 F01)] [(M04 F11):(M12 F07)] [(M02 F02):(M08 F08)] [(M10 F06):(M05 F12)] [(M09 F10):(M11 F03)]
[(M04 F08):(M11 F06)] [(M08 F07):(M12 F09)] [(M10 F10):(M01 F01)] [(M07 F04):(M05 F03)] [(M02 F05):(M06 F12)] [(M09 F02):(M03 F11)]
[(M08 F04):(M11 F10)] [(M04 F01):(M02 F03)] [(M05 F08):(M03 F09)] [(M01 F12):(M09 F11)] [(M10 F02):(M12 F05)] [(M06 F06):(M07 F07)]
[(M02 F01):(M05 F09)] [(M08 F10):(M09 F12)] [(M11 F04):(M12 F02)] [(M04 F03):(M10 F05)] [(M01 F11):(M03 F08)] [(M06 F07):(M07 F06)]
The ideal situation would be to play just the first 4 courts and all 12 rounds as this would give everyone the same number of games.