I had a black snake take 4 eggs out from under a broody at one time. It was probably around 3 feet long. It came back about three days later and got the other two real eggs under her and left the plastic ones behind. That was about 4 months ago so it was a lot warmer.
I would not dismiss the human theory too fast, but since it has happened the way you described, it is not real high on my list.
I had an egg eating hen. Mine left a mess and did not eat all the eggs, just a few.
I fed a dog a whole boiled egg with a pill inside the egg to get it to take its medicine. I could not just use the yolk as the yolk would crumble when I put the capsule in it. The dog weighs about 45 pounds and ate the egg whole. I've never had an egg-eating dog so I don't know know how much of a mess they might make, but this one is a food glutton and would not have left any mess from what I saw when she ate the boiled egg. I think she would eat a whole bunch too if they were available. Now I did peel the egg before I gave it to her.
My first thought is a dog, but fox and coyote are not entirely off my suspect list. I've seen both active during the day around here. A raccoon might carry them away to eat them, but I would not think they would eat that many. I'd really suspect a possum and raccoon would probably eat them on the spot. The hens could clean up any egg shell left behind, but mine usually did not with the egg eating hen.
I really can't tell you what it is. I can only wish you luck. Any possibility on borrowing a game camera?