Search to include ALL memberof changes EXCEPT for specific named groups

Searches are working good and some admins have alerts configured to send live updates as changes are being made. We have a new business process that is resetting group membership for a specific group on a regular basis. When that happens, it removes all members and adds members back in. This is triggering two notifications which is really considered noise by those admins.

We don't want to exclude Change Auditor from globally monitoring the service account that is making the changes on that group as there are other changes being made that are important to capture. So we want to be able to say in Search to include ALL memberof changes EXCEPT for specific named groups.

Has anyone run into this scenario before? The interface isn't leading me to a solution.