I've used straw, hay, and/ or shavings, have that 4" lip across the front of the nest boxes, and still have bedding rearranged and pushed out of the boxes! The feed bags give support and cushioning anyway, fortunately.
Mary
You might have someone pecking those eggs, so do watch for this. And I'd NEVER eat an egg I found already cracked in the coop. NEVER. One egg is cheap, and food poisoning is no fun!
Mary