I think you might want to rethink the light setup and modify the post processing to normalize the values. Perhaps the spotlights you are using are set to an extreme value.
Hopefully someone else can chime in on the subject!
Increasing the render resolution can reduce the need for AA, but unfortunately AA is applied at a screen level, it can only apply uniformly.
Also, increasing the thickness of the aliasing object can help, as the aliasing is mostly due to the specular highlight being less than a pixel thick. This is also why increasing roughness helps - because it widens the specular highlight.
Any details that are smaller than a pixel are prone to aliasing and other artifacts, so you can only either increase the pixels to get more detail, increase the size of the detail/decrease the amount of detail so that details are larger than a pixel, or utilize AA.