I'm not a vet either, but I do have a dog with food allergies.
My lab mix has been on several foods before we found Solid Gold. It has stopped them and she loves the food.
If the food changes you've tried had no affect on the symptoms and the tests your vet performed showed that your dog was allergic to trees and grasses and other things in the enviornment, I don't see how a Barf diet will be a solution to your problem - eating chicken necks is not going to change the way that the grass grows. Some allergies just can't be helped in that manner. My brother is allergic to dust and mold - nothing that he eats will change that.
I think you might need to do further research to determine if the treatments will help, what their side effects are and what a Barf diet will do for a dog with enviornmental vs. food allergies. I know when I have to deal with a medical problem, it is only when I have all of the information from many different points of view that I feel I'm ready to make an informed decision about what the best course of action will be.
Good luck, I know it is heartbreaking seeing them suffer like that! Boxer hugs to Chelsea.