Okay, I've managed, I think, to figure this out. Posting here in case someone comes along later and is frustrated by the same issue. One note: I've only worked with the upper body mesh so far, so I could be completely wrong.
First of all,
this thread kept me from going completely insane in the beginning. Of course, not rereading it when I started my adventures with the Surface Baking camera gave me a headache.
In any case, here's what I did:
Open up the female avatar object in Modeler. Make sure the select mode is set to polygons. Switch over to the View tab and look under the Selection>Maps button. In the little pop-up that comes up, choose Select Polygons from Selection Set.
In this next box, look for three lines labeled TextureGroup_something. These will select what you need for, well, each of the three textures. (Blindingly simple, no?) Now Edit/Copy, and then paste this selection into a new object. You should have just the part of the avatar you want to work with. With TextureGroup_Upper, I had to do some cleanup as it grabbed some of the head and lower body as well, but that wasn't horribly difficult.
Next comes the part where I forgot to refer back to the original thread.

With the new object, hit m to merge points. Also, with the Surface Baking camera it looks like you need to go to the Multiply tab and Subdivide>Triple. Otherwise there are some places where it just seems to give up when rendering and throw in black shapes.
Back the previous thread's instructions. Go into Surface Editor and select the material you want to work with. Make sure to check the Smoothing box. Now you can assign a texture, etc, as per the other thread. After this I save the file. I don't know if it's necessary in Lightwave, since Modeler and Layout seem to work together, but at this point I don't want to lose any work.

Load your object into Layout. Add lighting to taste. Make sure everything looks good in a normal render, then switch your camera over to a Surface Baking camera. Check your settings for the UV map, etc. You'll also need to give the camera a custom size (512x512 or 1024x1024). Other options as you like, and then F9.
One more piece of Lightwave voodoo I haven't figured out. Sometimes it gives me the image viewer, sometimes it doesn't. If it does, then I save the RGBA to a Targa. Open that in Photoshop, copy it and paste it as a layer in the PSD for that piece, in case I need to do any more tinkering.
Whew. It's taken me two weeks to get through that. Hope I can save someone else the work.