Spatial Join Layer Derived from Zonal Raster on Original Polygon

I'm trying to do a 1:1 spatial join between polygons created from the zonal max of a slope raster on the original zonal features. The problem is that the jagged edges cause the target features to overlap neighboring polygons as well so it just uses the first join feature in the 1:1 join.

So basically, in this picture, I want to use a spatial join to add the grid code 300 from the blue layer to the polygon (red outline) on the right and 100 to the polygon on the left. The overlap from the jagged lines are causing it to assign whichever value is first instead of whichever one has the greatest overlap.