It strikes me that an effective tactic against the Fedayeen who are taking up residence in sacred sites and hospitals is to simply cut them off. We don’t want to lay siege to the city of Baghdad as a whole, because that would be too hard on the civilian population, but there’s no reason that we can’t lay siege to a mosque.
If we can’t get the regime to capitulate quickly, I think the strategy should, and will be the same as in Basra. Go through and disinfect neighborhoods, relying on locals to finger the enemy, and gradually expand liberated areas. If we find enemy holed up and shooting at us, just keep our distance, and starve them out. Eventually they’ll run out of food, water, ammunition, or all of the above, unless they have an extensive tunnelling system with which to resupply from other hideouts. I doubt if they do, but even then, they still have finite supplies. We can maintain the high moral ground as long as we don’t fire back, even in the face of hostile press, at least with the American people.
We may risk whatever hostages they have inside, just as the Palestinians held hostages in the takeover of the Church of the Nativity last year, but at least it’s not the entire civilian population of Baghdad.
In short, I think that the current rules of engagement that restrict us from firing on sacred sites can work, at least over the long run. As long as the monsters are holed up, they have no control over the country or the populace. We can start to rebuild the country, even as we gradually starve out the vermin that have infested it for so long, just as we rebuilt Japan while continuing to find holdouts on Pacific islands for months and years, though I don’t think it will take that long.