My most favorite way of getting eggs in the mail.
Egg carton. Wrap egg in paper towel. Place in the egg carton, of course pointy end down.
Put a lot of newspaper in the bottom, place egg carton full of wrapped eggs in.
Place a lot of newspaper on sides, and top. Easy peezy.
When I get eggs wrapped in paper towels like this, I rarely, rarely, get a broken egg. And, I ordered a lot of eggs. Seems to keep the eggs real snug. I've gotten them like this with newspaper and the bubble wrap..both good ways. Just pack that newspaper in there to make sure the carton doesn't shift around.