After looking at the closeup, I realized I didn't use the right scale. The threads were too big. I changed it to .025. I also just noticed that where the lace turns over, the back side is rendering black. You need to turn on Normals Forward in the material there.

I rendered with smoothing this time. The shoulder looks much better.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)