It's in our group format that a group conscience can be called at anytime.
We come from a group that has its group conscience meeting once every 2 months in place of the regular meeting and everyone in the group is expected to attend. They vote on whether to discuss the topic or not and the chair person is only a time keeper. They go around the room and everybody has 1 minute to discuss the topic. Everybody gets equal share and there's no passing. This way, there's no politicking the meeting. Those with more education or those who speak more or those with more time cannot sway the meeting. The minority opinion is heard carefully so nothing is missed. They bet that God will show up and will be heard.
We are much smaller and just do our GC meeting at the end of the month. It's too bad that such an issue has to interfere with the recovery portion of the meeting.