Would using the next size up in diapers help any. It would also mean you could get them tighter because the tabs would wrap around better which overlaps the sides better.
Does the child eat a different kind of breakfast on daycare days such as a smoothy and toast instead of his usual cereal and juice. In other words it could be something he is having for breakfast that is too harsh for him. I mention the smoothy because I had one that had stinkiest poops not runny just stinky and parents finally discovered at home that when they mixed orange juice and milk in a smoothy she reacted. Either milk or juice was fine just not at the same meal.