One possible option is the swiss guided round robin. If the teams have rankings, seedings, or ratings you could have, for example with eight teams, 1-5, 2-6, 3-7, & 4-8. Assign pairing numbers so these pairings will happen in the first round. Don't follow the table from round to round but pick a round in which your leaders will be paired against each other. If you have groups of 6 and 8 you won't have to have a bye in each round and perhaps you will have the time for an ordinary round robin for the group of 6.
You might want to consider a swiss system or SGRR for all 14 teams, but that may have to wait until next season.