I would think you could use the process used to fast freeze fruit.Using CO2 (dry ice).
I believe that the yolk in the whole egg will break due to expansion (It's got a fairly thick membrane...haven't tried it but it's an interesting idea for an experiment) but that you can separate the components and freeze separately or scramble thoroughly and freeze.
You'd also want to freeze as rapidly as possible. I'm guessing that it would cause an unpleasant breakdown of protein and crystalization if it's frozen slowly. The general technique is to place a large amount of dry ice in a cooler with the prepared/wrapped eggs. I've heard of using a sanitized ice cube tray for portions. It's dangerous so make sure you read and understand all of the safety handling proceedures about it. It will give any thing it touches frostbite in a heartbeat. So use extreme temp gloves.
So you'd seal the eggs in the containers of choice (not too many per each which is why I like the ice cube tray method. lots of surface area for a small portion of egg) place in bottom of cooler with dry ice, seal the cooler and let the CO2 do it's work. I don't know how long it would take, but then when it's frozen solid, take cooler to freezer, and place frozen labeled eggs in freezer.
Like I said, I only use this for fruits, but I'm guessing it would work. You just need a source of dry ice and you could probably get away with refrigerating eggs over a week or two so that you could do a mass production.
Or, you could do some menu planning using the ingredients, like quiche, cookies, cakes, crepes, bread puddings..things that freeze well.