Hi - I'm really sorry that your dog is having so much trouble. It must be a very frustrating situation.
I also have a foot chewing dog (I don't think it is as severe as what you are describing with your guy). In my case it seems to be a seasonal problem and therefore probably due to inhaled environmental allergies although I have never had her tested.
You said they tested her for environmental allergies - did they also test for food allergies as well? Just curious about the results for that.