I don't imagine the NG is going to deploy with some insane RoE and only have lethal force. US troops didn't operate that way in Iraq (in theory..). So may not result in matters being worse. As for your scenario, no good is definitely coming out of that and I don't believe that is legal in Minnesota - deadly force is only permitted to save a life, rather than a TV.
I guess what you could do, is shoot the stuff they are looting. If you were a good shot. Or if you want a reasonable idea, you could just announce the weapon and people will just stay away.