Now that that question is on the table, what would constitute a win?
Since this ISN'T the highroad...
The best way to solve a problem is to eliminate the source of the problem. Unfortunately at times the problem can be so big that it becomes necessary to toss out the baby with the bath water.
Clean the place out. Nuclear or chemical (chemical preferred - the short term stuff so the infrastructure remains). Don't stop at Iraq - clear out Iran too. Let the buzzards feast for about 6 months or so.
In the intermission between destruction and waiting for the buzzards to do their job...
Let the rest of the unciivilized dictatorships in the world know they're next on the list if they decide to get froggy or complain too loudly. Tell the Euros to shut up and get back to watching their porn commercials on TV and keeping the sheople happy that make up their populations.
Once the buzzards have gotten fat, dumb and happy enough establish the area as a US protectorate. Setup something similar to the homestead laws the US had in the 1800's to encourage adventurous types from the US and Europe to move in and repopulate (if we let the Euros in it'll shut the greedy SOB's up) - however, no sheople allowed - homesteading ought to solve the sheople problem. Once the population levels reach some pre-determined point and the economies become mostly self supporting establish a US style constitutional republic and turn the area loose with guarantees of military protection and economic trade by and with the US.
In 25 or so years you'll have thriving, economically strong republics where there used to be barbaric dictatorships.
Of course this will never happen (no cajones and a congenital inability of politicians to see further into the future than the end of their peckers) and instead in 25 years we'll still be fighting the radical islamists. Oh well at least the times will remain
intersting.