I am excluding the church based on the church being a non profit organization that is not incorporated. Is this not correct? Control prong is always required- correct?
And you can believe me when I say I'd rather you ask the questions before making the wrong decision than beg forgiveness of your examiner later.
If the church is incorporated and nonprofit, it's subject to the E.O. rule, but does not need to provide info on the ownership prong (it has no equity owners). It will provide a control prong individual's name and ID info. If it is not incorporated, it is excluded from coverage of the rule altogether -- no ownership info, no control prong info.
If the church has a subsidiary (the school mentioned in your first post), the subsidiary stands on its own. Whether the church is subject to the rule or not will be irrelevant.