I have a feeling haveahart traps might work. I would put the same grain in the trap aas they are eating in the barn and place it close to where they are stealing the food. These traps will only catch one at a time and they will be alive. If the screen is too big and they get out I would wrap it with chicken wire or something similar. Snake food makes nice use of the rats. Post some pics of one you catch. I'm not complainng but have never seen a wild barn rat before.