Davidic line had to be based on the father-son genealogy and it had to go through Solomon (1 Kings 1:30). Only Solomon's line is to rule on the throne of David forever. (1 Chronicles 22:9-10). That takes Nathan out of the equation.
Being Jesus' stepfather is irrelevant considering that Joseph's royal inheritance was disqualified because of the curse (Jeremiah 22:28-30).
Besides, adoption is not an option in assuming the Davidic throne. There are other examples of this. A Kohane (priest) can adopt a son but that son cannot become a Kohane. The priesthood is transferred only by a physical (chromosomal or "blood") inheritance.
Besides, Jesus repeatedly told everyone that his Father is in heaven and not of this world.