So, four days of struggle to get some kind of OK-I-guess lashes. Some lessons learned:
When using a multi-resolution modifier and adding a particle system (i.e. hair) on top, the level of the preview has to be the same as the render level. The particle directions are based on the modified geometry underneath, and if the level where you do the particle editing (the preview) doesn't match the final render level, the particles will go shooting off in unexpected directions. Until I realized this, I thought there was some bug with hair rendering that only happened in the final render (and not when the 3D view was set to render the preview). I spent a couple of days messing around trying to figure this out.
You've also got to turn on the "use modifier stack" on the emission control panel or particles (hairs) will come shooting out of weird places and directions.
In order to paint vertexes in the weight painting mode, you need to select faces (or maybe turn the face selection mask off?). Otherwise, it just won't do anything, which is not particularly useful.
The "physics" panel on the particle system settings is not about the physics of the hair, but of the particles that direct the hair growth. So you want the physics on and Newtonian. Then you can set the emission parameters to shoot the growth lines more or less straight out of the skin surface, or whatever else you want. In this case I actually had a small "normal" component and a small negative-Y "object" component, to make the lashes point out of the skin and forward. After that it was all fooling around with the particle editing tools (see next point).
Combing lashes is a pain in the ass.
Finally, and this was an even bigger pain in the ass, I was (am?) reaching the limitations of my system and/or Blender as things started getting very crash-y. Rendering would crash a lot. Switching back to the 3D view would crash. Saving might crash. Eventually, I found that if I dropped down the level of the multi-resolution modifier, things improved. So it seems like it is basically caused by having too much geometry to render. However, doing that meant (because of the first point above) that I would have to start over, since trying to change the multi-resolution modifier with a particle system attached would mess up the particle paths or (more usually) crash.
So, Blender is amazing, but not completely amazing (at least on a run-of-the-mill iMac). And now I'm worried how much I'll be able to do with eyebrows and hair. Still, onward.