If these human shields are anything like their predecessors in Baghdad, they wouldn't be running into Najaf unless they thought that the fighting was over and they wouldn't actually have to put their lives on the line.
Yep, announce that they're all enemy combatants, and in 5 minutes we'll drop a MOAB. Then watch them scatter.
The real question - someone on the forum was saying this the other day - is why they are being allowed to go to Najaf. In some way, either the situation is out of control, or is being managed strangely.