This game desperately needs promotion. One of the best ways to implement this type of promotion would be to create a VERY basic in game ability for players to create tournaments for inhouse tournaments. Where players can be invited, and placed into teams on the tournament chart. The tournament will start at a specific time, all players expected to be present. Set by the host of course.

And you proceed. I think this would do wonders to help you advertise the game within its player base, help create a sense of need to learn teamwork for many players and teams, and give a real sense of ownership of the games dynamics to players.