Here's another approach to landing the egg safely -- a cardboard box with shock absorbing rubber bands to secure the payload.

In this vehicle, when the box experiences the jerk force of hitting the ground, the egg/CLUE will slow down more gradually by converting the kinetic energy into heat as the rubber bands stretch. This can act as an effective shock absorber!

Materials

For this vehicle you'll need:

Medium sized cardboard box
Rubber bands
Bamboo skewer, or similar
Scissors or snips to cut the skewer

Build the Suspension Rig

Use the skewer or an awl, nail, or screwdriver to poke a hole at the center of the box walls -- the sides, front, and back will do.

Thread a rubber band (or series of them looped together) through the holes, front to back. Use a small cutoff section of the skewer to hold them in place as shown.

Repeat for the side-to-side connection.

Secure the Payload

Wrap the CLUE in the rubber band intersection as shown.

Testing

Now, test the new vehicle by dropping it -- you should get a very effective reduction in g-force.

Note, a typical AAA battery pack may experience enough jerk force to momentarily jostle the spring-loaded batteries away from their contacts, thus causing a brown-out on the CLUE board. Here I'm using a LiPo battery to prevent this. You may be able to add tape to your battery pack to prevent this.

With safe, sub-9g results, it's time to graduate to a real egg! A couple more carefully applied rubber bands make for a good connection system.