I try to continue with the jaffe family tree as you requested. I use the site "ozar hachocma" and all the sources say that his father's name was Rabbi Moshe, and I don"t understand why he was deleted from the family tree.
True, there is no verification that Moshe's father was Rabbi Eliezer of Bologna, on the contrary, the thought is that the family's origin is Ashkenazi and not Sephardic, in addition, also regarding the explanation for the family name that he was taken from his wife name, Margola, I doubt it.