Well, I now feel like I'm getting somewhere. This is my Progress So Far picture, and it's a fairly extreme pose compared to what I've attempted so far. If you can't tell, she's sitting on a chair with her right foot raised so that it, too, is resting on the seat, effectively raising her knee up to face-level and bringing the long skirt along with it. It has zero poke-throughs and no areas where the mesh has turned ugly (unless you count the part that's crumpled up between her raised leg and abdomen but that's not even visible from any normal viewing angle).

Now... to find out how to change settings so that I can have tissue paper, lace, or rubber sheeting, and---most importantly---be able to simulate these fabrics without huge heaps of guesswork.