The last I heard DNA tests are unreliable. I'd skip that and use the money for something else. If you saw both parents, she has papers, I do not understand why you are questioning her status as a GSD. I don't understand your registration concerns either.
I've had several GSD puppies. (four) None of them have had the same coats as puppies. Even the long coats looked different from one another as puppies. They were all GSDs.