My solution is get make the southern Levant a single, secular, authoritative, elective despotate where politicians are elected by their credentials instead of a representative democracy; this way, the government is much more likely to stay secular than if it was a democracy.
I suggest that the state be of the citizen-state type, not a nation-state, shall be ambivalent with regards to its citizens' beliefs and nationality; this is not possible for a nation-state but, being that a citizen-state is at its heart based on reciprocal obligation between the state and its citizens instead of on ethnicity and culture, this is perfectly possible. In the new southern Levant state, anyone who follows the state's laws, labors for it and is otherwise deemed to be useful to the state, can become a citizen regardless of ethnicity. I also suggest population transfer for social harmonization and homogenization.
The economy of this state is to be based on tourism, R&D (much like Israel already is), education and to a lesser extent secondary industry. Tourism alone should easily suffice, given the huge importance of Jerusalem to Abrahamists.
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Learn the patterns of the past; consider what is not now; help what is not the past; plan for the future.
-Myself