Sandy, I've never dyed any vintage piece before, but other members have, I believe, had some luck in doing so. But, in the past I've had excellent luck with using permanent, black wide-tip fabric marker on a very large swath of discolored acetate taffeta lining in a dress, and in touching up small areas on the outside of black dresses. The lining job matched perfectly! But, I would worry, on an area as large as what's on your dress, about a marker not matching the matte finish of your dress, or the black not matching exactly.
I don't know what I'd do in your spot.... it's a quandary. I think I'd go to the fabric store with the dress and see if I could find a dye made for delicate fabrics that doesn't need to be "set" at as high a temperature as other dyes, and maybe try to spot dye the areas (feathering into the good areas) so as not to get the item soaking wet. As Amber says, that can be problematic. Or I might try a marker or touch-up fabric paint and see what I could do with it. Even if you can't match it exactly, but could blend something in to those areas so as to make the piece wearable...
Or, sell as is and let the buyer figure out what to do. Hopefully someone will come along who has had success with this sort of work.