Make it less socialistic and economically sucessful.
Economic situation of Arab regimes seem to be definitely decoupled from evergreen Western dilemma of "market vs. socialism". Taking into account conditions they operated in, Socialist Syria is not traling Capitalist Egypt, if at all. And "Conditions" mean "foreign meddling". So in order to change fate of "Arab socialism" we need to change the ways foreign powers meddled in the regional affairs. IOTL lines (although, taking into account regional conditions, they definitely were "lines in the sand") were very firmly drawn according to basic formula "West supports Fundamentalist Islamists, Commies support Modernizators". Arab Socialism never went farther than Scandinavians (or Socialist French) in their ideology, but they picked wrong master.
So we need to couple one of dominating "Arab Socialist" regimes of the day with Western country which does not have seizures every time words "universal health care" or "social security net" are uttered. Then, once USSR is fallen, this country can organize "palace revolution" to replace upper levels of other "arab socialist" countries, who "disgraced pure ideal of Arab Socialism by cooperation with Communism". I propose French-Iraqi alliance (those countries closely cooperated IOTL), supported by Swedish. Then Hussein organizes carefully orchestrated regime change in Syria in 1990 instead of OTL Kuwait escapade. Taking into account that OTL regimes of Algeria and Libya are Arab Socialist today, half of the region is "Socialist".
Yes, but in a way that Israel doesnt fall. Its a major rallying point for Arab Socialism, after all, and hence "needed", in a way.
Major? Make it "cornerstone". Although I would pity Sadat/Mubarak regime and kings of Marocco. Tunisia and Jordan if one of Arab Socialist countries really manages to deliver near-fatal blow to Israel. Those "Western Puppets" will be swept away.