I have a Staffordshire Terrier (your dog's "cousin") with very similar sounding skin issues. I have tried a lot of things too, but not nearly as much as you have or for nearly as long. With my dog Roxy, I have found diluted Apple Cider Vinegar sprays twice a day really
help with the rash. We originally treated Roxy for mange with shampoo, Revolution, and antibiotics last October even though we couldn't find any mites on scraping (didn't find anything
unusual). This completely fixed the skin issues, but once off the antibiotics the rash came back. After that I suspected food allergies, so switched the foods around a few times. She seemed to have bad reactions to some foods (Orijen/Acana), and not so bad with other foods (Iams of all things). Fish is highly suspected as an allergy. I tried environmental changes like shampoos, laundry soap (tried plain washing soda among others), changed bedding materials...environmental things didn't seem to make a difference one way or the other.
I started spraying Roxy (2 months ago?) with the ACV solution twice a day and was able to eliminate the rash from Roxy's body, armpits, and belly. So, yeast infection? Bacterial infection? Allergies? Topical ACV can help with all
of that so it doesn't help to identify the problem, but it does help with the symptoms! She just has redness between her toes now which I can keep under decent control with once daily spraying. For now, I'm feeding her Acana Wild Prairie grain-free food that she appears to be mildly allergic/sensitive to (possibly the fish content?). I have been wondering if Roxy's system would learn to tolerate the food as time goes on if I am able to control her reaction to just a mild reaction. Maybe wishful thinking. For now, I'm keeping her on it at least until I can flush her system of all the other things that have been bothering her. I'm considering other diet options now, trying to pick the next step.
Omega 3 is a natural anti-inflammatory and also significantly helps to increase immunity. The best way to supplement Omega 3 is wild fish/salmon oil of good quality. Find something that specifically requires
refrigeration or is in capsules otherwise it is likely fairly rancid even before it is opened (gotta love the dog food market). I find human fish oils in capsules to be cost effective and high quality. Roxy seems
to have issues with fish/salmon so I am unable to use these oils for her (although I haven't tried since I started the ACV, so I should try the fish oil again). Flax oil can also be used, but doesn't work as well for dogs. I started Roxy on Platinum Performance which is a broad-spectrum supplement providing high omega 3 (flax), protein, vitamins, and minerals. This product is well tolerated by Roxy and is quite reasonably priced. I noticed I had to cut down Roxy's food a bit when I started the PP, so I imagine that it would probably help with your dog's weight. There is only one Canadian distributor, Summit Performance Products. www.summitpp.ca
I had a dog in the past that couldn't maintain weight on a raw diet. I think it was the lack of carbohydrates to tell you the truth. A simple diet that is also cost effective and easy to make that you could try is 1/3 meat (cooked, raw, partially cooked doesn't matter), 1/3 frozen mixed veggies (beware of corn though...may or may not be tolerated), 1/3 brown rice. Add to that a well rounded supplement like Platinum Performance and you are golden. Mix it all up in a batch, put into serving-size portions in little freezer bags. Pull a baggie each day to thaw, add the Platinum Performance and voila. It is simple, easy, has limited ingredients, and is still nutritious.
I find keeping things simple helps big time! Not only does it help the pocket book, it helps with peace of mind, and it also helps to differentiate which foods/supplements/topical stuff are helping and which are not.
Here is Roxy's story if you care to read it all. http://www.pets.ca/forum/showthread.php?t=78956
I hope this helps, and good luck!