Partial Success

So I'm still definitely having blending issues.  But a considerable amount of the time, the program behaves well.  In the first shot here, you might be tempted to think everything was ok:

But even in this one, you can see a couple lines where things are messing up.  This next shot was taken some time shortly after that, and it has obvious problems:

On a positive note though, these shots do show my "billboarding" math to be performing fairly well; the particles all face the camera pretty much.  They do have different shapes though because the four points that make up the borders are processed through the perspective transformation, but arguably that is desirable.

Now I must inquire more deeply into blending and depth buffers and such matters so that I can get to the bottom of this ugly line business!