I don't seem to be able to reduce the whiteout much. I keep darkening both the spec and power maps bit by bit. This screen shot is with almost black power and spec maps: each map is set to roughly a value of 18, where 0 is pure black and 255 is pure white:

It looks a little better if I disable post lighting, but not enough to make a difference. Besides I want these skins to look good with POST lighting enabled.
EDIT: Just created pure black spec and power maps and tried them out under same sun angle (taking off W from A116 on CraterMA at 10 am). Full-power auto climbout.
These are pure black maps. So, zero specularity and power -- the least amount of reflected light, set to the widest possible dispersion a skinner can effect on a skin. I'm thinking the sun is even more powerful in AH than I'd realized.

I'm adding the maps I used just in case I've set them up incorrectly, or have them misnamed or something and they aren't really working the way I thougth they were supposed to.
EDIT x2: I also deleted both spec and power maps and let the skin use the default maps. It produces the same whiteout under these conditions. I suppose I could try darkening the diffuse map by 50 or 100%?