Sorry for getting back so late! Again, thanks for all the interesting and informative replies. It goes without saying that one can only reasonably balance one color temperature at a time and that sceneries with sunlit areas and shade have at least two distinct color casts. Still, the area where color casts seem to have the worst effect are skin colors, where a blueish cast can ruin the whole shot for me (unlike I want a sad and dramatic look like in the image of my crying daughter in the theater).

The reason why simple filtering of the developed slide doesn't help is the small latitude and the saturation characteristics of slide film. While the medium tones clearly exhibit the blue color cast, the bright tones show it to a much lesser extent, since the excess blue simply saturated. Skilled post production workers can surely save that frame, but that's not the point of shooting film imho. Yes, Ilfochrome is certainly a thought worth pursuing eventually, depends on whether I can locate a dark room nearby where they are at least willing to let me store the necessary chemicals.

If an 81C filter can get me in the ball park then that's what I should probably look into rather quickly, as the weather still isn't all that sunny around here

Allow me few more comments:
@2F/2F: My shots are neither portrait, and certainly not glamour (it's my baby daughter, not some random chick showing excessive skin). They are holiday shots including the surroundings and members of my family. My ambition is to eventually achieve nice landscape shots with members of my family included as compositional elements. The reason this whole thread ended up here is because the main subject was skin color.

@keithwms: I started shooting Astia recently, for the very reason that skin colors tend to go haywire in other films if the light is less than perfect. But I sure do like the bombastic colors that E100VS gives me in sun light and I also sure like the at least 2 extra stops Provia 400X affords me. If an 81C filter allows me to get similar results in slightly overcast weather (plus the clouds avoid the nastly shadows in the faces) I'd be happy as a clam.

@Sim2: My problem appears in both E100VS and Provia 400X, so it doesn't seem to depend on which vendor makes the film. And it's not black magic either: in overcast weather the light has a strong blue cast which of course shows up in the resulting slide. There may be a slight difference in Kodak colors vs. Fuji colors, but it's not nearly enough to offset the blueness of that light.