Here’s the scoop on this business — counterinsurgency campaigns sometimes succeed, normally when you have a state repressing an internal insurgency. Very, very, very rarely you see a foreign power successfully crush an insurgency and then organize a “decent interval”-type pause before departing (see Britain in Kenya, South Africa). You have essentially no instances of foreign power demonstrating an ability to stay put over the long haul.
Stepping back, you need to ask yourself questions about goals. I mean, say we did have a method at our disposal for crushing the Sunni Arab insurgency in Iraq and entrenching SCIRI or the Sadrists in power in Baghdad — why would we do that? Would would it accomplish? Just “winning” doesn’t do anything unless you’ve picked a battle worth winning. I’d love to see Iraq become a shining democracy, but (a) it’s not going to happen and (b) counterinsurgency has nothing to do with it.