For the Sultan/the Empire, come up with a compromise which leads to Zionist Organizations assisting in improving the empire's fiscal situation. Co-opt Zionism so that the whole of the Ottoman Empire is a Jewish homeland, rather than concentrating the Jews in one province where they can have nationalist aspirations.
The official Jewish organization of the Ottoman Empire (mostly Sephardic, IIRC) pledged at one point to make Turkish the official/predominant language of Ottoman Jewry.
IIRC there was a saying that the only people in Austria who were Austrian were the Jews, everybody else was German, Hungarian, etc - so providing refuge to Jews, making them learn Turkish, and coopting them into being a fiercely loyal pro-Constantinople group throughout the empire could work well for Constantinople. There already were Ottoman Jewish organizations, so propping them up to subsume Zionist ones would probably be good for making sure Zionists complement the status quo rather than challenge it.