just to add, if you decrease your min shading, you still have to decrease the shading for that item or group.  it won't change anything (as far as i've observed) just to decrease your minimum shading rate because the object or group shading rate trumps it if the local one is higher.  i've also found the shading rate is render size dependent. it actually gave me really bizarro errors with depth mapped shadows when i was rendering at a medium resolution.  i had to raise my shading rate to get the depth mapped shadows to blur properly.
in your Nefertiti image, i noticed grain in your shadows.  bagginsbill probably has much better advice than i, but you might make sure you have your pixel samples high enough.  and i think your filtering high enough and on gaussian?