Hello, I'm sorry to hear about your pup.
Allergies are the most common cause of itchy skin. I'll give you an allergy rundown of likely causes for skin troubles. He may have more than one allergy given how symptomatic he is now. Dogs that have one allergy often develop several with time. The effect of multiple allergies aren't additive, they actually compound one another.
Even if you don't see fleas I do recommend using protection, if only during the late spring/summer and early fall months. They are the most common allergen and it only takes one bite a month to make an allergic dog scratch so I recommend using flea prevention even if you never see one again. Frontline, Advantage or Advantix are excellent but some dogs do react to the alcohol or carrier ingredients. Don't use over the counter products, especially Hartz or Sargents, as most are ineffective if not toxic.
Other allergens can be inhaled (like grass pollen, dust mites or molds) and you can use a combination of antihistamines and high doses of omega-3 fatty acids to help with those (they also help with the symptoms of flea allergy). In combination fatty acids and antihistamines work synergistically, much better than either one alone. If his symptoms worsen seasonally I would think that inhaled allergens are a part of his problem. Unfortunately given the mild winter most of the country experienced and early spring allergies will be much worse this year.
You can try
1) Benadryl (diphenhydramine only don't use the combo products as they can be toxic) at 1mg to 2mg per pound or one 25mg capsule per 25 pounds of dog orally every 8 hours. I see that you have tried Benedryl but don't know if you used a high enough dose. OR
2) Claritin (loratidine) at 5mg per 25 pound dog once or twice daily. OR
3) Hydroxyzine at 1mg per pound orally every 8 hours. OR
4) Chlorpheniramine at 4mg to 8mg per dog once or twice daily Some dogs do better on one antihistamine rather than another.
You'll have to see which one works. Most dogs respond to Hydroxyzine the best. Give each a week to 10 day trial and if it isn't working try another. Be aware antihistamines can cause sleepiness or hyperactivity in some dogs. These side effects do wear off with repeated use.
Omega-3 fatty acids are fish oil products. 3V by DVM or Derm Caps ES are good brand name products. Use the high end of the dosing schedule for your pup's weight.
Cool water baths with an oatmeal shampoo or chlorhexiderm shampoo (which is antibacterial and antifungal) and a conditioner with an antihistamine may help. The water rinses off allergens and the cool temperature soothes itchy skin.
Food allergy is possible. Dogs with food allergies tend to lick and scratch their paws, face and ears the most, but any of the "allergy reactive areas" can be affected. You could try a true hypoallergenic diet like Hills z/d or Purina Veterinary Diets HA rather then the limited ingredient diet you have tried so far. No treats, flavored medication or bones while on the diet and it must be used for a least 12 to 16 weeks to see the full effects. There may not be anything wrong with the food he is eating but if it has a protein or carbohydrate he is allergic to in it he will react
A secondary bacterial or yeast infection on the skin will cause him to be even itchier and with the scabs and dark skin you describe I suspect this is possible. These occur when a dog itches and bites himself and breaks the skin allowing the skin's protective layer to be broken and a secondary infection to thrive. These can be diagnosed with a skin swab and antifungal or antibacterial shampoos will help. I like a shampoo called chlorhexidene shampoo as it is antibacterial and antifungal and gentle enough to use daily if needed. You don't need to wash everywhere daily, just the affected areas. Make sure to dry his paws very well after bathing and rinsing. If these infections are present then oral medication (antifungals or antibiotics) may be needed to get it under control.
Cortisone ointment applied to the very itchy places twice daily may help as well if needed. Some sprays have alcohol which can be painful on raw skin and lead to more inflammation. I don't like oral steroids but topicals directed at the problem areas can be very helpful and are less likely to cause side effects.
Another option if the antihistamines and omega 3's aren't enough is a product called Atopica. It suppresses the immune system a bit so it decreases allergic symptoms but it doesn't have as many harmful side effects as systemic steroids. If you are interested discuss this medication with your veterinarian as it is a prescription.
If it's been a while since his skin was checked for parasites like cheyletiella or sarcoptes they should be looked for as well as both lead to very itchy skin.
Probiotics are very helpful for replacing good bacteria in the gut but don't help the skin much.
Autoimmune skin disease is possible. The best way to diagnose those diseases is via a skin biopsy, but he should have gotten better with the steroid therapy your veterinarian prescribed as autoimmune diseases are steroid responsive for the most part.
I know skin disease and allergies are frustrating. Most cases cannot be cured but I do think we can do a better job helping your fellow be less miserable.
Please let me know if you have any further questions.