Well heck, here's Conitec's answer, which I only found, ironically, after Googling!

Q. I have problems with the sorting of transparent or TGA images. For instance, I'm trying to make a tree by crossing two sprite like a 'X. When using TGA sprites, the first sprite always draw before the second sprite. This doesn't happen when I use PCX or BMP sprites.
A. Transparent objects can not write into the z buffer, and thus are simply sorted according to the distance of their origins. This does look wrong when they overlap or are close - when you think over it, it's logically. You just have to make your 'X' from 4 separate sprites when using transparent textures.

So it's sorting according to the average distance away of that particular chunk of the model, as opposed to the relative distance away of one piece to another.

So, according to this, if you have an "X", and the corners are 1,2,3 & 4 from top left, clockwise:

1 2
X
4 3

and you are at "1" corner of the X, then the far side of that same line of the "X", "3", will render before "2" or "4", even if they are closer to you than "3".

This seems odd. Is there no way to fix this? The "improved overlay" code in the wiki doesn't appear to do the job. And if there isn't a way to fix this, can anyone suggest a quick and easy way to break up a complex model (like a tree) into chunks, and still retain the skin mapping?