I believe you are mistaken in your comments on blood. The terms used in the text are common phrases used in English to indicate genetic relationship. They all imply that the protection on Harry is because of the love of his mother and his acceptance by his mother's sister.
To suggest that the magic of the protection is literally only in the liquid flowing in his arteries and veins, rather than in his whole person, is to mis-read the book because you so want to make it match what you want it to match.
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