YOur vet is right
For the poo (which for many of our dogs is the most yummy treat EVER... (I don't agree there is an enzyme problem)) you just need to manage the situation to keep it away from your dogs.
One of the many reasons most of us crate train is because it just naturally teaches our dogs to NOT get into the habit of eating/destroying household items because when you are in a crate those items are NOT available. So grazing on the house never becomes either a habit or an issue.
What you may want to work on is training for a great 'leave it'. Best and easiest is if you do it with a clicker... Intro to Clicker Training (perfect for puppies!)
Generally, all the behaviors you are seeing are coming from a bored pup with too much energy, too many brains, and NOT ENOUGH TO DO!
I know for my dogs I have to sit down with the calendar and actually SCHEDULE!
Schedule dog classes (really, classes). It doesn't matter what classees, obedience, rally, clicker, agility, herding, tracking. ANYTHING to get the dog out of the house and both of us learning something new and fun.
Schedule socialization. With friends. With neighbors. With the new people I met in DOG CLASSES. At dog events in the area.
Schedule REAL exercise. Hiking. Swimming. Canoeing.
It's amazing how the more I organize and plan my dogs days, and put it on the calendar..... the better my dogs behave around the house. Cause when they are home they rest and relax. And they focus their brains and energy to do 'good' when out and about with me, rather than get into trouble around the house cause they are bored bored bored.
Your situation is normal!!! And why, frankly, I don't recommend GSD's to most people because for most of us with extremely busy and over schedules liives already, adding all those extra hours just for the dog isn't possible and it's the dog that gets the short end of our time and money plus weekly planning.
Not saying that's you.... just most people I know.