Are you totally sure about it not being seborrheic dermatitis? I know you said there is no distinctive smell to her skin, but sometimes the classic profile is not shown, and this can happen with many issues, not only skin issues.
Have parasites been ruled out? I once had a dog who became very itchy, slightly greasy but there was no bad smell. It turned out he had been bothered by "harvest mites" in the summer grass. That was what the vet thought anyway. I can't clearly remember what his treatment was (this happened many years ago) but think it may have been a cream of some kind, plus a shampoo. I don't recall the shampoo had any negative effect (such as making his skin dry etc.)
I guess mange has been ruled out too? It is quite easy for any dog to develop demodectic mange. Our vet always called it "fox mange", and it's easily picked up in country areas or grassy places. A subcutaneous injection cleared that problem almost immediately and there were no lasting effects.
However, mange also has a distinctive "mousy" smell. Not necessarily unpleasant, just distinctive and slightly musty.
Allergies of course are another thing. It's hard to discover what can cause an allergy.
His diet sounds good, so doubt if it's any food allergy unless she is allergic to one of the meats/fish she eats. Such things are not impossible. I have heard of dogs being allergic to beef for example. And I suppose it's not impossible to become allergic to anything no matter how "healthy" it is. But you could bit by bit eliminate some of the meats one at a time, by excluding that for a week or so, see if there is any improvement or not....etc.
But that is a slow process of course and can take a number of weeks.
Occasionally endocrine problems can cause oily itchy skin too. So do check that. But a blood panel should spot any imbalances.
You can try bathing her skin with a 50-50 mix of apple cider vinegar to boiled cooled water. You can also try green tea! Or make a mix of the two. But test it first on a small area of skin, wait 48 hours before trying it on a larger area -just to see if it suits her. It might or might not help.