A good "event planner" in charge of the church calendar should take care of such conflicts.
I believe the church in business session should decide on what evangelism is done. More than anything else, it will help them to "own" it also and be more willing to work at it, be a part of it. I generally do this with the women at the church in that I have a meeting to discuss what is to come. It works really well, I get great support that way.