Hi

Sorry you're having such trouble finding out what's going on with your rescue pup

I will say though (and please don't get mad at me for this) I checked the other threads you started about this (think I saw 5?)only because it sounded really familiar to me (I didn't look through them all but I'm pretty sure I commented on one of them) and it seems you
did get a bunch of advise.
I personaly (if I recall correctly) suggested that you should try experimenting with limited ingredient holistic foods with the protien source being something out of the ordinary (like venison or duck for example), have you tried that?
I know it's very frustrating when you spend a ton of money at a vet and they can't give you answer, but I'd also suggest you try a different vet. Not all vets are great and some of them can miss something that another one will find right away. Your other option (although I understand it's expensive) is looking for a veterinary dermatologist. They will give you a definate answer and if they do suspect a food allergy, they can direct you in how to preceed (it's all about process of illimination and can take a long time to discover the culprit).
Again, not trying to sound mean, but you've gotten a good amount of solid advise here, have you tried anything else? I'm not sure what you're looking for by posting alot of threads about the same thing since Feb., no one's going to have a miracle answer for you, but we have given suggestions, what have you tried and how did it go? Like I said, if you're frustrated here and don't like our suggestions, try a different veterinarian or a specialist.
Good luck