How To Stop Skin Tones From Changing

[TLHEADSHOTS]

I am shooting outdoors, natural light, portraits, using skrim and reflectors, shade lighting . I am using AWB because the colors are more flattering than with custom. But when I change tops on my model and backdrop colors...the skin tones change, and sometimes they change drastically.
1. Is there anyway to lessen the change of skin tons?
2. Does anyone one out there prefer CUSTOM WB to AWB? (when I have compared AWB to custom, I prefer AWB. My custom shots had a blue or grey cast. versus the AWB shots were warmer.

[another view]

If you're shooting RAW, then shoot the first one with a grey card in the frame and use that to set your white balance later. If you're shooting JPEG, then a custom white balance would be best. One little trick for custom white balance is to put the translucent white plastic cover from a can of Pringles in front of the lens (like it was a filter). Shoot the white balance of the scene with this and it will work out pretty well. Doesn't cost much, anyway. There's something called the Expodisc you can buy that does this too, but it's expensive.

It's a little like shooting in manual exposure mode - if the background gets lighter and you're in an auto mode then the subject (whole frame) will get darker, etc.