If you have a vacuum bag sealer, you could make some custom bags that hold two eggs or more, crack the eggs into the bag (a wide-mouth funnel helps), vacuum out most of the air and seal them. Lay them flat during the initial freeze and they will store great!
On an episode of BBC’s: Planet Earth I saw an eagle grab a small goat, carry it off a cliff, and dropped it. Effective to be sure and kind of clever for the bird, but terrifying to watch.