I sincerely appreciate the feedback I've gotten. My main strategy has been to "salvage" a lot of the red images by making them monochrome, or using the color temperature trick to turn the images a more purple color, as others mentioned, which can be desaturated a bit and not have as bad a "pink and white" look. If there is presence of any other color to a slight degree, it makes this trick work much better. I do shoot RAW so that gives me a lot of options for improving the look of the images.
One thing that still puzzles me -- why is red the most problematic color rather than blue? For making a grayscale image out of RGB, the formula 0.299R + 0.587G + 0.114B is common (it's what the YIQ color system used by analog TV used for the luminance). From this, you'd think that since blue contributes the least to the grayscale, that it would be the problematic color. However, if something is lit with only blue light, the pictures come out great. Why red?