Welcome to the forums
I am not informed enough to be able to advise on vitamin toxicity, effects from same &/or protein levels giving skin problems - though I am aware that some specific protein sources might not agree with some individual dogs.
Your post has a fair amount of info re your dogs past & present which is great to see.
It might be useful if you can provided some more info re current problems..........
What exact food brand and variation of same was your dog on when you first noticed the skin problems ?
How long was your dog on the food fed when you noticed the skin issues ?
If your dog was absent of skin issues when you switched to this food then how long before you saw issues ?
Did you make any other changes at or shortly before you noticed issues ?
How do you know if skin issue is down to primary food or one of the other items mentioned as treats or extras ?
How do you know what specific protein sources cause issues for your dog ?
What protein sources cause issues and what are the specific issues ?
Can you rule out all other non diet issues (clinical conditions, infestation, coatb thickness, heat, environment, dog initiated agitation, meds reaction, stress, anxiety, weight etc) ?
I am NOT infering or suggesting any of the above are factors but whole picture arguably needs consideration.
If food sources are sole issue ( & you indicate several dietary variables), I see it two ways to tackle this.......
Option 1 : If safe to do so, go back to what was fed well before any issues. If dog skin issue goes away then and only then consider stepped changes whilst carefully monitoring dogs skin.....go back a step at 1st sign of any issues.
Option 2 : Identify a different good quality food with a likely non issue protein source....then feed that solely (no different treats etc). This gives a blank canvas. If no issues keep dog on that.
Whchever option chosen, only introduce other food sources one at a time & a!lowing some weeks in between each change so as to monitor health after each change/addition.
If it were my dog it would be option 2 all the way - This approach in my view the quickest way to try to help your dog.
Some have found skin issues pretty much sorted by simple steps such as adding a supplement, coconut oil or maybe adding a couple of sardines every so often.
You may wish to get dog clipped if desireable to see what is going on under there. If not doing so I would consider susing a really good organic type non-irritant shampoo suitable for your dogs skin condition.
Maybe also look into natural remedies - I don't know enough to begin to properly & safely advise you but we had some success re dry skin ear tips on a dog using some carefully diluted tea tree oil. (Never use this neat) .
I have not recommended a particular food. Feel free to seek viees on any shortlist or particular foods.
I am not a pet nutritionalist....so please treat my comments accordingly.
HTH & Good Luck