As I said in the remark there is no book comparable to the Russian edition of Hurwitz-Courant (Evgrafov was the editor of the Russian translation who improved the original very much).
There are 2 comprehensive Russian books covering much of geometric theory; both exist in English translation: Markushevich and Goluzin.
They do not have the theory of compact Riemann surfaces, like Hurwitz-Courant, but Shabat (which you like) also does not have it. I would say that Markushevich is a good replacement of Shabat. Goluzin can serve as a source of graduate courses.