Update- I used CLR, and it was FAR better than the Lysol Bathroom stuff I used to use. It sort of gelifies the scum and then a stuff bristle brush, it was done. I used the CLR on my floor too, and it was clean as it has ever been. For giggles, I tried the brakekleen on the tub too- it DOES work, but with no windows in there, I felt the fumes might put me on a flight I can't afford.
SO- for my type of scum, whatever it may be, CLR works fantastic.