My girl is going through the same thing, but her allergies started before the raw feeding. She scratches her belly and underarms, bites her flanks and hip bones.
Her kibbles were predominantly chicken based before, so after two weeks on chicken I'm switching to turkey. Costs over double what the chicken does but it was amazing to watch her chow down on her first turkey neck - thanksgiving came early for my girl ^^
I'm going to switch her to pure turkey for a week and see if there's any improvement. Vet ruled out all the usual suspects so I'm stuck with dietary or environmental. Chicken is the easiest protein to obtain but I'm really hoping its the culprit - environmental is so much harder to eliminate.
I hope it goes well with your pup!
EDIT: My pup just had two consecutive bouts of mucus-y diarrhea like you described, one last night, one midday today, I just started her on turkey necks this lunchtime so I don't think its that. Hopefully its the chicken causing these symptoms.