To add another, lesser known brand of kibble to research: Beaverdam. Now available through major retailers like Amazon, Chewy, etc. It’s a bit more like horse feed. Comes in a plastic feed bag with the paper/string pull top.
http://www.beaverdampetfood.com/products/dog-and-cat-food/
FWIW, my dogs have an environmental allergy/irritation that has nothing to do with their food. I chased a LOT of food trials and diets with my first dog. That was The Thing to do. Grain free, no chicken, fish-based, limited-ingredient treats, etc. Turned out he was super allergic/sensitive to flea bites and his flea preventative was no longer effective.
I’m grateful to be off the limited-ingredient bandwagon and I have landed on something that works for my household throughout the year. Now I treat my dogs like garbage disposals and we are all happier for it.
Good luck! I understand the helpless feeling of watching your pets itch and be miserable. You will find something that works for your household.