Crusader States
Interesting scenario. I imagine that the Venetians and the Genoese would be constantly quarrelling over trading rights.But an instable crusader state in Egypt is still better than a stable Muslim state there. Taking Egypt out as a hostile power is the best way to guarantee long-term surviving of the crusader states. And if the crusaders hold onto Sinai, Egypt is pretty secure from outside as well.
Another important bonus for holding Egypt: this should open a secure seaway to India. The return on Indian trade could be enough to literally buy safety for the Egyptian crusaders.