It sounds like it's getting worse, not better with avoderm. I'm not sure which flavor of IAM's your trying, but lets say your dog is allergic to chicken and there is more chicken in avoderm then Iams, since it's a better food.
That's why it can be why it's causing more of a reaction, compare the ingredients. If the ingredients are comparable, you might need to switch to a different protein type food..
California Natural (makes a few flavors) of limited ingredients.
Also, to help combat the poop eating add some
digestive enzymes into the food.