All of this we will never know. The cuckoo feather patterning can be very prolific once it's introduced, as it has its advantages (camoflauge/breaking up outline against predators). No reason to say the Dominique Game Bird was not bred from the American Dominique, not the other way around.
I think if we could go back in time we would find that perhaps one man used a Dominique Game fowl (or what his neighbor said was one), another man used a Scott's Grey, another used some cuckoo jungle bird from his second cousin's shipment into the country from South America or somewhere else. If these men got together they would all say "why yes, I have Domineckers, those cuckoo colored little hens - they lay me lots of eggs, raise their own brood, I eat the extra cockerels and they're healthy little birds".