From the photos posted it's kinda hard to determine a cause. The droppings do appear to be in fact crap. What kind of crap? Iv'e seen a lot of crap over the years but I'm not sure what kind. I have eliminated ( pun intended ) larger animals like elephants etc.. however. All kidding aside. Consider posting one of those motion activated trail cams to seem if it is in fact some type of animal. Of course if it's bigfoot and you get a good pic you could just buy a new lawn with all the money you make.