;fSunShadowUpdateTime=1.000 default - amount of time transitions take;fSunUpdateThreshold=0.500 default - frequency of shadow updates
I would suggest lowering fSunShadowUpdateTime to a very low value, relative to fSunUpdateThreshold but above zero. At zero, you lose all fluidity since you don't see the shadow move.
I have tried to find a setting that results in a slow, steady movement of the sun shadow, but two issues prevented it from looking presentable in my opinion. First, the shadow border will always be a blocky mess due to the poor quality of shadows in general. I think the only way you could overcome this is to reduce shadow distance so low that it would only be good for close-ups. Second is the timescale the game uses; at a timescale of 30, the sun's shadow moves too quickly and it begins to feel like time-lapse photography.
fSunShadowUpdateTime=0.000fSunUpdateThreshold=0.100
I use these values. They are certainly not optimal, but they result in me not noticing the movement of the sun's shadow (unless I'm staring at it), which to me seems to be the point. The updates are instant, which mitigates the blocky rendering of the shadow line that you would see with more frequent updates.