Wow! Great job, I don't spend the extra money on those foam sheets but they are really nice.
When shipping 12 eggs I use an egg carton. I cut a piece bubble wrap and put it in the egg cup, then the egg, the bubble wrap should by about 4"x4", I then lay a piece of bubble wrap across the top of the eggs the extra wrap will fold over each egg. This will make the carton very hard to close so if it is to resistant, I cut the top off and reattach it directly over the eggs and tape the entire carton closed. I then wrap that in a foam cloth or bubble wrap. I place that carton diagonally in the large Priority Mail box 12x12x7. The corners have more protections with filler this way. I have used shreaded paper, Foam peanuts, Crumpled paper and crumpled grocery bags either plastic or paper. I think the Plastic ones weigh less and can possibly keep you under on your postage weight if you are right on the border between one pound and the next. The key is to keep your eggs from moving at all. and provide plenty of buffer between any edge or side of the box.
My son works for FedEx and they carry US mail by contract now. When the mail sacks come in they are literally dumped from the plane into a carts below. No mater if you put Fragile on the box or not they are all handled the same at that point in time as any other mail. They do not intentionally throw and try to damage boxes marked eggs or fragiel, they never have an opportunity to ever see them. Once on the conveyor belts they scan sort the boxes but they can fall off before a person ever handles them. The eggs that are lucky enough to be in the middle of the large sacks or on the bottom have less chance other things falling on top of them and will arrive to you in better shape. When packaging your eggs just make sure you have as much buffer or shock absorbing material as possible in order that your eggs can withstand the bumping they get when the planes are offloaded. The smaller the airport the smaller the planes, the shorter the drop and the better your eggs will fare.