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.