As long as we rely on local Iraqis for HUMINT, many of these thugs will roam free. It's their home turf. The insurgents are fully aware that HUMINT is our weak link. They've infiltrated the local police and have without doubt acted as phony informers. Not a single Iraqi in that town is to be trusted - yet we need to be able to trust somebody if any kind of precision action is to be taken.
Once you insist that war has to be a "precision" operation, you have made war impossible.
In my scenario, no HUMINT is necessary.
After enough time has elapsed to allow escape from the city, Fallujah become a World War II urban war zone with the emphasis on artillery and air power.
What about the civilians who are dumb enough to stay behind?
They win a posthumous medal: