I wanted it big, so I made it 375% bigger.  The threads are still a pain however I made 13 of these and they all worked with some trimming.  You simply tapper the beginning and end of the thread on the lower section so when it locks in you can take it apart.  unless you want it almost permanent to play a trick on someone.   If the egg was tight for the little kids, I did slightly sand the threads with a green pad and apply a bit of wd40.  After running the egg open and closed 2-3 times it started to break in and become user friendly to most everyone.  You also may notice that the lower egg is 1% or so smaller. This was because I didn't want to change my printer's calibrations for a bad file.  I was also not wanting to design this from scratch as I had a week to print out 13 of these.