How to reduce extra sharpness at the edges?

I'd dupe the layer, blur it enough to reduce (Gaussian, Median or whatever works), change the layer blend mode to darken, apply a midtone adjustment to lighten slightly and or playing with blend if sliders. Finally, creating an "edge mask" using find edges filter, or glowing edges filter or a custom convolution filter matrix is another option to isolate the darkening of the halos to height contrast edges. This could all be automated/semi-automated into an action.

I haven't tested, but the Camera Raw Filter sharpening has an edge mask feature and it may support negative values.

It's long winded, but if you use the clone tool set to Darken, on a new layer also set to Darken, it won't overwrite the subject.  It obviously depends oin the tonal values of the subject and backgroung.