You sure it doesn't come from Chernobyl or Fukushima?
There's gotta be something to do with it other than decorating...
Lets think about this scientifically.
Fog is the even exposure of the silver crystals all over the film. The fog is at the bottom of the contrast curve. As the fog level rises, you tend to loose part of the exposure curve that always keeps the same angle for a given development. So we have a film with a very shallow exposure latitude but regular contrast under normal development. If we over develop, we just make the fog layer more visible by converting more silver in the negative. So we need to underdevelop the film to keep the fog at a minimum of visibility. It will always be there, just less present. But underdeveloping will reduce overall contrast at the same time. A massive overexposure would be needed in order to put most of the image in the highlight section, but you will experience some clipping on both the bottom (shadow) because of fog and at the top (highlight) simply because the curve tops off at that point.
We know the film can produce something, not a lot but still there is a bit of life left in it. So exposing at maybe EI3 and developing for ½ the time in C-41 (no point in spending on E6 here) might be a good start.
What you can do is shoot a few frames at EI 3, just anything out the window for a test, take the camera in the dark bag, open the back and using some safety scissors cut a bit of the film and process just a few frames. Readjust and then test again. At least you won't be wasting good chems.