I'm sorry to hear your dog has this problem that has been so difficult to resolve.
If he's seen the vet, has ringworm been ruled out, because your description could indicate this fungal skin infection, which causes the hair to break off at the root.
I'm glad to hear he's been on Natural Balance's limited ingredient diet; his most recent symptoms like scratching under his chin and licking the fur off his paws, could be due to allergies, or also could be a reaction to stress, from something that's changed in his environment or due to his skin problems.
If he eats/drinks from a plastic or stainless steel bowl, change it to glass or ceramic, as the other materials can cause allergic reactions. Also, think about his bedding, where he sleeps, lays, etc., and he could be exhibiting an allergic reaction to the detergent/fabric softener you use to launder his bedding, your bedding, cleansers used on the hard floors, carpet shampoos/powders, scented candles, air fresheners of any type (spray, solid, plug in), cologne, hairspray, etc.
I think you'll find this information on skin allergies and other conditions in dogs, helpful:
Yes, because of all their 'wrinkles', Shar-Peis need extra grooming to keep all the areas within the folds, clean, but what you describe now, does not sound like a 'usual' Shar-Pei problem.
I hope you're able to get this under control, with the help of your vet, and the information above. You might need to consult a veterinary dermatology specialist who would have a better perspective on your dog's problem.
I wish you and your furry boy all the best.