It renders fine.

In Preview mode:

1. For the Egypt hair, the diffuse texture gets used as the transparency map no matter what I do.  Even if I go into the advanced mode and change it, it will use the diffuse texture.

2. For the M3 beard, the transparency maps only appear if I put them there manually, either in the simple or advanced modes, and unlike the Egypt hair, they stay there.  They just don't have any effect in the Preview mode.

I only have one Runtime.

Transparency display is set to "Enhance multiple transparency".

So, the final render of either hair prop is fine.  It's just that I have to do a render to see what it looks like because I can't see any kind of transparency changes in Preview mode.  And that's what I want.  And I don't understand why I can't have what I want all the time. ;-)

I seem to remember a long time ago, I had the same problem with a prop.  Just out of curiosity, I saved it as an .OBJ with a new name and then imported it again.  I applied the diffuse and transparency maps to the new .OBJ, and they worked!  I suppose I could try saving the hair figures out with new .OBJ names, but then I would have to edit the CR2 files to point to the new geometries, wouldn't I?  I've never done that before.  I don't even know if that would work.