The problem with doing something to the egg such as coating it in something, is that the egg is usually given to you just minutes before you drop it, and you must be able to pull the egg out of your device when done to succeed.
The best projects I saw were the ones that didn't try something fancy, but just secured the egg inside some absorbany material and some other material on the outside to reduce the impact... something to intentionally break or smash...
I saw a project done in 15 minutes before leaving for school succeed, while a project that was built over a span of a week fail miserably.
Parachute designs usually fail because there isn't enough time for a chute to open and fully catch the wind, and people always built the chutes too small. In relation to the size of chute needed to stop in the 2 or 3 seconds before it hits the ground, a chute would have to be pretty big.
Get a smallish box... fill it with those sealed packing bags of air, put the egg inside making sure that it can't slip out and hit the cardboard, then wrap the box very loosly in quilt stuffing (the kind that comes in sheets, not puffs) and voila. Instant success.
Success favors at-home trials, although throwing caution to the wind and finding out the hard way is a bit more fun!