ThAt is a lot of pooping going on. What are you feeding and when?
It is clear to me how long the dog is left home alone. The longer the time period the more difficult to get all toilet activity outdoors.
My experience says a dog can go 8 to 10 hours easily without being able to relieve body functions, I say that with the experience of a person who has a dog that goes to "bed" about 10 PM and stays sleeping or resting until 8AM, or 10 hours and even then the dog isn't in any urgent state to go outside.
Different breeds my vary on the above time estimates.
The only way I know to train a dog is to impress on the dog the need to go outside. This is best accomplished in you case if you can catch the dog doing his "business" and can express displeasure and then take him outside. Simply taking the dog to the scene of the crime and being sure he reacquaints himself with the poop,then to scold and take out side. Some will argue against this approach and you may get their view. I don't buy in to the hired training approach, but I suppose it can help...hire a dog trainer.