I won. Well, technically Pam won, but I'm taking credit for it
Seriously though, she did find the solution, posted above, it did work in the end.
I can also report that, after all the effort, I got better results by simply using the blending setting. I'm not sure why the shader didn't give as good a results (not even sure what was different, but you can tell watching it), and other parts of the project are more important, so I'll figure it out some other time.
I would however suggest that if anyone needs to do fade effects, blending is probably the easier and better way to do it (Pam can correct me if I'm wrong, but I think blending is just a function of the default shader anyway?).
The game I'm working on will be out in March, you can see where I used it then (it's pretty obvious and right at the start).
...and so I said to Mr. Gates: "$640 billion should be enough for anyone!"