It's not upside down. It's at a 45 degree angle. If you cut out the bottom of the carton, they'll just sit there.
I though it was upside down too. I flipped my laptop upside down, sideways.... now I see it. Loving the carton idea.
I don't turn each egg one by one anymore. I just run my hand over all of them and sort of shift them around. No problems so far....
Good Luck with your hatch!!