arcgis desktop - Merging attributes from point with containing polygon?

I need to develop a process for merging the attributes of each point in a SDE feature class with a polygon in a SDE feature class that contains the point to create a third feature class. The third feature class should contain the attributes of the point with the geometry of the polygon. This seems to be a spatial join. Is that assumption correct?

The points represent incident locations. The polygons represent counties. The team is requesting I intersect the incident with the county to create the third feature class. There will be multiple incidents per county so they expect to see a row for each incident and the county geometry will be repeated.

I've been using ArcToolbox > Analysis Tools > Overlay > Spatial Join. Setting the Target Feature to the incidents layer and the Join Features to the counties layer yields the correct number of rows but the geometry is a point. I need a polygon. Switching the Target Feature and Join Features yields the correct geometry but not the correct number of rows.

How should I be approaching this?