It may not be worth the money, but I wonder if a tailor could add a layer of that tan bathing suit liner fabric into the pre-existing seams? Might also end up causing friction problems but I wouldn't think it would be any worse than adding a layer of underwear.

If they're uncomfortable seeing you in the white, they should've taken that into consideration before choosing that color! Make 'em deal with it

(and thanks malkin, now I have "clammy chamois" stuck in my head!)