I added one of Illustrator’s stock art brushes to the edges of the solid shapes. I think this is pretty much The Right Look. I’m not entirely happy with how the edges look, but I can make my own art brushes later.
I kinda feel like the fact that I finally figured out how to make this project work in Illustrator is some kind of landmark. I’ve had the techniques I use here sitting around in my head for a good while, but I finally put them together today. Now the only excuses I have for not doing this thing is “busy with other projects”.