Since you said his stools are soft and he eats it, I thought maybe it was his dog food. I feed my dogs Nutro also, and they do very well on it. Maybe a vet check is nessecery just to rule out any health problems. I recommend keeping your eye on him all the times, as if he was a little puppy again. Don't let him have full rein of the house until he stops going inside. Sorry I really don't have much advice other then keeping him with you at all times to correct him in the act.
Hope he's trained soon enough. Good Luck.

Your exercise plans sound very much like Cesar Millan is always telling people! I'm reading his book currently.