If the roosters are New Hampshire and Delaware, I would not expect either one to have recessive white or extended black. The Delaware would have white barring.I don't see any reasonable way that could be from Recessive White genetics.
So if one hen was black, hiden by recessive white, she could produce a black chick like that. Barring could be either from the hen or from the Delaware rooster.
I agree with your explanation about how Dominant White could be involved, just saying that recessive white is also a way for a white hen to produce a black chick.
With only one black chick, I'm thinking there is just one hen producing that color, and she did not produce many total chicks. I presume she is either one of the White Rangers or else one of the White Plymouth Rocks. I'm leaning toward the Ranger, because it sounds like there were fewer Ranger hens than Rock hens, but I'm not positive, and I'm not sure whether she is actually Dominant White or recessive white.
Did you post it yet? I can't seem to find it.I'll post the genetic path this weekend...