After some additional review, I believe that the Mechanical Fatigue Tool (FT) is working as expected with negative mean stress S-N curves. I had some flaws in my original model that I corrected.
If the specified Stress Component is a normal stress, absolute maximum principal stress, or signed von-Mises, the FT maintains the sign of the mean stress. If the dominant stress that produces the mean stress is negative, the FT uses the appropriate negative mean stress S-N curve.
If the specified Stress Component is maximum principal stress or von-Mises, the FT does not maintain the sign of the mean stress, because those stresses are always positive. Thus, even if the dominant stress that produces the mean stress is negative, the FT uses the specified Stress Component (which is always positive) and uses the appropriate positive mean stress S-N curve.
I checked the FT results against Ansys nCode DesignLife results. They are producing equivalent results for each of the stress components.
How the FT handles absolute maximum principal stress can be a bit confusing, because the AbsMaxPrin stress is always positive. The FT is able to maintain the sign of the underyling principal stress. So, if it uses S3, it maintains the negative sign for the mean stress.
It was an interesting question that required some digging on my part to verify, but I do not believe that filing a bug report is needed.