After breakfast, egg plate clean up
I feel you pain. I spent 2 summers cleaning dishes to help pay for summer camp and that was only 100 campers (3 meals a day). 800 eggy dishes is not fun! 

Getting egg off doesn't require anything special, just a soak in cold soapy water for a few minutes. Egg is a mix of protein and fat. Fat comes off better in warm or hot water but proteins come off much better in cold or cool water as heat makes the proteins stickier. If you can, set aside a container of some kind with cool soapy water and put loads of the plates into it. Soak as long as you can, then pull them out a few at a time and wash the gunk off with a sponge, then get into the dishwasher right away. If you're scrubbing you're working too hard!