Hmmm...rice isn't really an allergen, but anything is possible I suppose. Since she had sensitivities to the treats - I would check those (looking back) for wheat/corn/soy, it could be those ingredients in the treats rather than the protein. Even though chicken can be a more common allergen of protein sources, it would be less common than the things I mentioned - but it could even be the chicken.
As for that poo, a little mucus at the end may have just been her anal glands emptying, which is a good thing. It may also have been from adding olive oil to the diet.
I'm wondering if she could have dry eye - esp. w/ the vet's comment. Then, it gets itchy - she scratches it and the skin starts to get irritated and loses fur (that scenario was similar to Wylie's, but from a diff. cause). Did the vet mention dry eye at all?
One more thing, since you're homecooking - are you balancing the cal-phos ratio? If not, it could also be that her system is a little out of balance.
Either way, I'm so happy to hear she is improving!!!