"Well, it's got to be done in a way that allows us to believe we aren't monsters."

Well the UN peace keepers aren't monsters, are they?
The miltary knows know how to "perform" like UN peace keepers.
The UN way of doing something is could be a safer approach for the soldiers.
They are many ways of doing things- instead of a minute perhaps you should think about for a longer time.

It's no accident that casualities in this war are relatively very low.
Now, you can argue about tactics. You could argue that if the US miltary, had "simply" decided that the US miltary should be feared, the Iraqis might have decided that suicide bombers and the like would have been a fairly useless tactic. Anything remotely looking like a threat is simply shot. Shoot people because they look hostile- you only have to do that a few times and the word gets around. This isn't what the American soldier IS and has been traditionally- so this is a fundemental problem with this approach. But if you look at the wide range of options, we didn't have to use the America soldier. Using the America soldier is expensive- you *could* "out source" this. Now, we don't generally hire mercenaries*- they are not the same thing as an US soldier, and it wouldn't be popular idea for US public or the US Miltary. But if you wanted to do this war differently, and if you didn't care about all the ramifications of supporting foreign merc armies. It would be possible to promote, package, and sell this un-American approach.
You could say that the emphasis on low casualities, the legality, and "joint-ness" of this war is "about" selling the idea that a mercenary approach is not neccessary and unwise; and to prove that the American Miltary Model is the only viable approach in war fighting not just for America but whole world.

* The soldiers who were killed in Fallujah were mercs- members of US guard, hired by private company after returning from duty from Iraq.