Thanks, randym77. Stew did a beautiful job on the rat's fur, and I will try out his render recommendations, excerpted here for completeness:

"I found strand-based hair looks best with mapped shadows, a high number of pixel samples (7 or more) and a gaussian or sinc post filter of size 2."

In the meantime, I have found that setting the dynamic hair to be invisible to raytracing greatly speeds up rendering, although the figure's ground shadow then looks disconcertingly bald. To compensate, I increased the light's Shadow Blur Radius to 5, which makes the ground shadow blurry enough that the "baldness" isn't apparent.