How about encourage and support the new Caliphate. Once established and they have their wonderful Islamic Republic, see below:
With them unified under a leader or council we can then begin to "negotiate". Wars are fought between States with uniformed Military. The situation now is impossible because they are with out form, a ghost. In their religion they must participate in pilgrimages to enter heaven. i.e. The Kaaba in Mecca, Saudi Arabia, Masjid al-Nabawi in Medina, The Al-Aqsa Mosque in Jerusalem. Mount Sinai. The Imam Ali Mosque and Imam Husayn Shrine also hold high significance. There is no such requirement in our religions, so the negotiations would go something like this: Every time your "terrorist" venture outside your new "country" and attack the West, we will nuke a holy city. Soon they will be unable to get into heaven without donning a radiation suit that is...
Turkey had the Arabs sorted out for 500 years.
I favor restoring the Sultan, and the Caliphate centered in Istanbul.