The correct strategy is to demand reciprocity. For starters, no more immigration -- none -- from Moslem countries that do not recognize freedom of religion, free speech, the emancipation of women, etc. Go on the offensive in every forum. Tell the muzzies that we are not interested in "dialogue" with any culture that does not meet us in a free marketplace of ideas.
I don't think it matters what the level of enlightment of any particular Moslem country is (although some are clearly worse than others). The terrorists who came here and have gone to other western countries to work their evil are not influenced by an enlightened or what we could consider semi-enlightened governments within all of Islam. In fact, they act out against their own governments and people as well as sending terrorists to the western world. Many of the exported terrorists have come from the more moderate Moslem countries, such as Jordan. I think we have to deny entrance to anybody from any of those countries for the time being, period. Certain people passing extensive background checks might be let in on tourist visas if there is a system in place to monitor their movement. To do otherwise would alienate the moderate Moslem countries. But we simply can't let them in to wander off and get lost in the country at will. I think a moratorium on student visas should be enacted until we have full cooperation from their native countries, including western Europe, and the means to fully investigate and track these people and limit entry to diplomatic and tourist visas. I certainly don't want the French to be allowed to export their mossie militants here.