You omitted the healthy dose of Lumbee blood line that is mixed in.
Let's not forget the Turks. Portraits of the great educator Sequoia show him wearing the uniform of a Turkish sailor, complete with turban. A number of place names ascribed to native american words have similar meanings in Turkish. Kan tok -- full of blood. Kentuck -- bloody place.
IOW, there appears to have been a great deal of traffic crossing the Atlantic before 1607. c.f. the Piri Reis maps.
The native american peoples seem to have peacefully adopted a number of other outsiders.