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At this point, I thought back to Poser's hair room. I stopped using it long ago, as it was always such a witch to render with. But, knowing the speed and quality Carrara delivers, I decided to give importing a Poser file a try.
I applied just over 110,000 hairs to a sphere, changed the number of verts per hair from 20 to 10, tweaked the root, tip, and highlight colors, and brought the file into C5.
I actually used somewhat higher settings than I did with the previous test, and still the renders finished in under half an hour, (under 20 minutes for the second two shots here). There were not enough hairs to completely cover the sphere, but changing the ball's color from the default gray to a dark blue helped tremendously.