Wow! That is a LOT of eggs!
Souffles will use a lot of eggs and you can make plain cheese, spinach, broccoli, mushroom, chocolate ...
Spanish tortillas use a bunch of eggs too, and recycle well from dinner to breakfast and lunch.
The advice from @Soupcon to sell the eggs for baking is very good, but more for your farmers than for what you can do with your bounty. Our government, unfortunately, frowns very hard on cottage industries that involve any processing of food, even that minimal.
Even the producers will probably have to find a commercial egg processor who can use these pullet eggs too small for marketing in the shell. It would be easier for the the farmers, probably, than trying to locate enough individual bakeries or restaurants willing to buy the small eggs still in the shell. This 10,000 egg per day thing is not going to resolve itself overnight. At least they might be able to recoup some of their investment now, and it would be very hard to even give away that kind of surplus of eggs which will just keep coming every single day. Disposing of them in that quantity is a stinky and unsanitary proposition too. Sheesh! They need to look into finding a licensed processor ASAP, or get set up to do it themselves. You do not want half a ton or more of egg waste per day disposed of on your land.
Such a shame, too, pullet eggs are great!
They might find a way to sell some of them to farmers markets and give some to food banks, but you are not exactly in a high density population area, and I'm not even sure unwashed eggs are legal to give to food banks. Our benevolent and all-wise government hates that centuries-old practice as well, and insists eggs be washed and then need refrigeration. 
And Shelby, you really do not need to refrigerate eggs that have not been washed. There is a protective barrier deposited, that if you leave it alone, you can store them for weeks at room temp. I'm writing to you tonight after having consumed thousands of these eggs produced and stored this way on my grandparents' small free range farm. This was way before free range was a "thing" or cool. Grandfolks also ate these eggs all of their long lives and died of old age, and nothing related to eggs. Grandpa would often eat half a dozen pullet eggs for breakfast, and he lived to 78. 
