I used to snicker a little when I read these threads -- no more! Rocky has also taken up this gross habit. None of mine ever did it before, and I couldn't even imagine it -- til now.
I don't know the answer either. Rocky doesn't really eat them so much as play with them. I find bits and pieces as he has obviously drug them around. It seems to happen the same as you say, when I am not here or asleep. I did catch him playing with one so I know it is him. Not sure how a product to sprinkle on the poop is going to help. Instead of sprinkling something on it, I would rather pick it up and flush it.
He is good about using the pads, but seems to suddenly get the idea that he will drag one around and bite it into small pieces. It really spoils puppy kisses when you know he has just had poop in his mouth! I will be interested to read the responses you get. Maybe we can both find something to put an end to this nasty little habit. I almost did not want to admit it! My dear, sweet, loving little guy plays with poop! arrrgggghhhhh!