Video conference for a leadership meeting in a Mission

In the Chile Osorno Mission, every Friday after transfers we hold a leadership council for all of the Zone Leaders and Sister Leaders. Due to the large scale of our mission, some leaders cant physically come and particapate via transmission through vidyodesktop. In doing this we have various issues with broadcasting the sound because the program vidyo desktop only accepts one sound input at a time. The council is vary fluid and all are invited to speak from their seat so the use of a solo microphone is imposible. In looking at various options I ask myself the question if it is possible to use the church sound system and broadcast it? I Imagine that it is but we are all unaware of how to do it. Is it possible to connect a laptop to the churches sound system, utilize all of the church microphones and transmit it to other buildings? When doing this will the sound come through the other buildings sound system or will it come through the computer that the missionaries use in that building?

We used multiple microphones, connected to an audio mixer. The output of the mixer was connected to the meetinghouse sound system, and also to the microphone jack of the laptop used for the webcast. We could have also connected the mixer output into the audio/video capture device that connected to the USB port on the laptop.
If we didn't have an audio mixer, we could have used the audio output jack under the Sacrament table, which we have used in the past to attach a tape recorder.

A tabletop conference room mic won't work?