As I said, use gelatine, it might work! If you poor it in the box with the egg inside it(in the middle), and make it cool down, it will become solid, which means its a rubberish thing with the egg inside of it, you should seriously try it.
Yeah, you're going to want to have it so the egg doesn't have room to move inside the straws and the straws shouldn't have room to move inside the part of the bottle so layer some tissue inbetween the bottle and straws too. You want to create something that absorbs an impact equally around itself and the egg instead of a specific point. Spreading force over an entire area rather than a localized point is what is going to save your egg from breaking.