Transitioning to a higher protein food can take longer than 1 week. And for some dogs you just have to take baby steps depending on the healthy (or non-healthy) state of their digestive tract. I was feeding poor quality food (1 star foods) for about a year or so then transitioned them to a “middle of the road” type of food like Merrick and Castor and Pollux and Blue (all regular with grain) for a couple months and then started incorporating grain free/mid-high protein foods. The final transition to Instinct took about 2 months for one of my dogs.
I didn’t know about probiotics or digestive enzymes back then either which would have helped alot. My fosters get a moderate protein diet (Nutrisource grain free Lamb) and I give them ground psyllium for just a couple days for fiber and give them probiotics for their gut and they usually transition without diarrhea. I also find that wet foods don’t have much fiber so I will add some fiber to that too or chia seed.
You might consider a limited ingredient diet for a little while to give his bad digestion a break and start giving him a multi-strain probiotic.
http://healthypets.mercola.com/sites/healthypets/archive/2013/05/22/pet-probiotics.aspx?e_cid=20130522_PetsNL_art_1&utm_source=petnl&utm_medium=email&utm_content=art1&utm_campaign=20130522
http://probiotics.mercola.com/probiotics-for-pets.html
