I use a 'roll away nest box, they are brilliant, and yes they do stop the eggs getting broken and out of sight (and getting pooed on )
I would recommend them highly (you can either buy 'em from the auction website or make your own ) the ones on the auction website are very well made, just need a drop of paint or wood preserver on them, I bought my first one there them made my own after that
(but to stop the 'egg eater', it might be a case of 'blowing' an egg and filling it with mustard, chilli sauce and let them eat that, but I have tried that, it didnt work, but after they stopped laying for the winter and started the following year, they never ate them any more or showed any interest in them)
A fake egg might work
Ref the soft eggs, I did have that problem,
I made up a porridge of layers mash (just add warm water) and mix in a couple of teaspoons of small oyster shell grit, I give it in the mornings, its lucky if it last 30 minutes,
I also 'cook' egg shells, grind them up into a sort of dust (in a coffee grinder) and add that to the porridge (someone here mentioned this about the egg shells)
So far I havent had a soft shell egg so far (I have had some huge eggs and funny shaped eggs though)
Give either a try, got nothing to lose (and the hens might like the porridge)