Without Genocide, Nuclear War, or Forced Conversion to Christianity on a scale never before seen, I don't think this is possible.
There are only a two small areas that might be able to break 90% Christian and view themselves as European without some extreme acts, but not the entire Middle-East.
Lebanon - If it retains the borders of Mount Lebanon Mutasarrifate, with only the addition of Beruit. Probably the easiest.
Oran and vicinity - Oran peaked out at about 85% European IOTL (though about 10-12% of that were Jewish). Perhaps have the Treaty of Tafna hold, so Oran remains an exclave of France detached from Algeria, and receives a little more immigration than OTL, allowing it to become 90% Christian at some point (the Jewish population could be a bit lower without the Cremieux decree)
If you allow Population transfer's some more area's might be possible (part of Galilee, the Mitdja plain of Algeria, Greater Casablanca).
The problem with your scenario is the extremely high Christian percentage required. Lower it down to 60%, or even 70% or 80% and the challenge is much more tenable.
If you remove the Christianity requirement, I think you could end up with all of the Middle East, sans Egypt and Turkey (and possibly Syria) view themselves as European and be integrated with Europe.