Even though Chaim is (apparently) debarred from entering modern Israel, it occurred to me that modern Israel is not the same thing as biblical Israel. When the Torah says that Jews should live in Israel, it's arguably referring to biblical Israel which extends a few miles into what is now Egypt. Looking at a map, it seems that much of the Egyptian city of Al'Arish is within the boundaries of biblical Israel.
Since Chaim's mother is Egyptian, Chaim can probably claim Egyptian citizenship and move to Al'Arish thus legally fulfilling the commandment that he should live in Israel.
Obviously he would have to keep a low profile if he moved there, but the fact is that most Arabs are not downright hostile on a day to day basis. Unlike certain other groups who can be found right in New York.