If you're ever at a team building exercise, and the contest is to build some sort of contraption to protect an egg that's going to be dropped..
Go with the cone parachute idea. It's the only one that really works.
Make a cone out of a piece of paper. Shove a piece of paper in the bottom of the cone. Insert egg. You may want to insert another piece of paper on top.
Then, attact straws to the top of the paper, which you attach to another piece of paper, which you use as a parachute.
Yes, this idea might be expensive. But it works. Unlike trying to wrap the egg in straws.