A few months ago, someone across the bayou from me started selling their eggs for 2.00/doz....one dollar less than me. I refused to go down on my price. Some customers stayed with me. I learned that my eggs tasted better. I figured it was because they had more grass and bugs. I kept the customers, but had to do more trading than selling for a while, which was fine with me. Less selling, but also less buying. We ate a lot of seafood and deer for a while.
I will not have a price war. If I go down on my prices, I am just selling eggs because I love raising chickens and GIVING eggs away, because @ 2.00/doz, I won't even be able to replace my chickens when they stop laying. I need to be paid for what I do.
As to washing in very hot water; some of my customers have bought my eggs as hatching eggs. Also, I don't always put the eggs straight in the fridge. I might want to incubate, so I can sell chicks and raise my own meat birds. Thats how you really come out ahead; by looking at the big picture. Eggs alone and you might not make it, but when you consider the free fertilizer, lack of need for a lawnmower, very cheap or even free meat, you have a very profitable project.
Check what you have to do, but I can't see very many people will go around and enforce it. Maybe things are different where you are from. Since 1986, no one has ever inspected me or questioned any aspect of my operation.