Frank...(10 years after the fact)... if you haven't found this information since your posting, the problem with your theory of a dutch mother is that Anthony was referred to as a "mulatto" in:
The records of New Amsterdam from 1653 to 1674 anno Domini New York:Published under the authority of the city by the Knickerbocker Press,1897,2765pgs. P Stuyvesant; P L van die Grift; Will Beekman; Oloff Stevenson; et al......,
On page 1_204, Anthony Jansen, "mulatto", a lawsuit against William Strengwits for wages owed concerning two months of labor. Anthony won the case.
I'm not convinced of the Mullah connection, though.