How to create a center point from multiple features grouped by an attribute

I have a large data set that has been read from multiple autocad drawing files. At the current stage each feature has an attribute "project_num". There are many feautres (usually lines) for each project_num. I would like to get this down to a single "centroid coordinate" (preferably center of gravity) for all of the lines from each project_num.

CentrePointReplacer will generate a single point for every feature.

I tried FeatureMerger but am having problems. Both the Supplier and Requestor are set to "project_num". I have set the Feature Merge Type to geometry and checked "process Duplicate Suppliers" (build polygons) but get the same number of merged features as the input. If I use the "group processing" option, I still get the same number of merged features.

My current workaround is to use the DuplicateFilter before sending it to CenterPointReplacer. I have also tried creating a point cloud from all the resulting CenterPoints and then running CenterPointReplacer on the resulting point cloud.

I'm thinking there is a better way to do this!