I hear ya' on the nasty scent. If the smell is in the vinyl, it may not wash out. And Kimberly's right that you shouldn't put baking soda and vinegar in the same cycle, but I would try them in separate cycles where they won't neutralize each other. But they are both good odor neutralizers.
I always encourage consumers to contact the manufacturers of products that have negative effects on consumers. You know that if you're getting asthma from this doll, other moms and children probably are, too. Fisher Price should hear your preferences. There may be a toll-free number to call, or websites always have a "contact us" option.