As soon as we stopped feeding the duck-based food, his stools firmed up, within a matter of only a couple bowel movements, I'd say. We didn't do the gradual transition from the duck to the lamb, because we didn't want to keep feeding him food that might be bad. Besides... he was already having diarrhea anyway, so the sudden change wouldn't make that any worse! Because we changed the food so quickly, we noticed an improvement right away. It did take a little while for the stools to be completely "normal," since it obviously took awhile for his body to get rid of all the traces of the duck in his system... but as soon as we stopped giving him the duck-based kibble, we stopped having to wipe his butt with cottonelle wipes after every bowel movment.
As a side note, the SD I/D the vet prescribed for us was the soft canned food... which is beef-based. Good thing, too, if the dry kibble is poultry-based!
One of the reasons I switched to the lamb-basted TOTW, besides wanting to be sure it wasn't from the same batch of food as the bag I suspected might be bad, was that the lamb-based one had a bit less fat. I had thought another possibility was that the foods we'd been feeding him might just be too rich. It sounds like the EVO is a very rich food, so that could also be contributing. I know in Lerwick's case, the main problem was definitely the poultry... but the extra fat probably wasn't helping.
He's doing great now. His whole digestive system is much hardier. He can tolerate treats, where before we couldn't give him anything (we still avoid poultry-based treats, of course), and he no longer gets diarrhea when anything remotely stressful happens (a trip to the vet, meeting a loud/agressive dog, a car ride, etc.) and before we could be sure that the next bowel movement would most definitely be full-on diarrhea. Now he has normal stools every time... except he did have one soft stool when he first came home from being neutered early this month. Even then, the stool wasn't "pudding" like it used to be, and every BM since then was normal.