I haven't dealt with ASCAP for a long time, but I believe their method in a case like yours is to deal with the venue, not the organizers. (Venues stay put, organizers can easily vanish into the suneet.) In your case, the venue is the church.

Have you asked to see the correspondence from ASCAP? What is ASCAP asking about? for? Have you volunteered to help respond to ASCAP?

Do all the top people of the church know what kind of music you are doing? Have you reassured them that none of your performers are doing ASCAP stuff? What are you doing to assure compliance from performers? Have you told the church what steps you are taking?

I see that your first post says you do 'traditional' stuff. That's a very vague term. A lot of people would say that songs such as

Green Leaves of Summer
Puff the Magic Dragon
Where Have all the Flowers Gone?
How Great Thou Art

are traditional, but I'm sure they are all copyrighted material.

What you need to do is to ensure that old songs performed are public domain. 'Traditional' isn't adequate.

The church has been doing your group a favor. Now it's time to help the church in return.