Okay, I've made soem progress in tracking this down. I know that it is not the tga itself that is causing the problem. I was able to load it into my level as a sprite withut any sorting problems, even with 4 of them lined up--the sorting worked fine.
So its my model.
Here's the thing--I'm importing from a .x model format (as exported by "TreeMagik").
Can anyone think of a simple/quick fix or workaround that doesn't involve breaking the model down into a bunch of smaller models as suggested earlier? When I check the model in MED, it appears that the mesh is all "open" as opposed to closed (whether that emans anything, I don't know). All other settings on the model's skins seem to be in line with what has been suggested here.
As per my link further above, I do have a copy of that model in md7 format in case anyone would care to take a look at it to see if they can spot what's going on.
Much obliged--thanks!