How about this:

Set a limit on how many can join each team.

I'm not sure of a good number because I'm new to Fellowships, but lets say for example 20 people can belong to each game in a fellowship. Lets say one of the team members do not actively play in their game in the fellowship, the Big Boss (or Captain) can remove that user and open that spot up to a new person.

So if someone really want to be in a chess team, and it is full on one Fellowship, he would have to find a new fellowship that has an opening.

I don't know if limiting the number of people to one fellowship would be good - you would get some of the current fellowships full, and new members would never get a chance to join & chat in their.