It already exists! If you look at my earlier post on this thread, it explains how all of this works. No breed has more eggs to begin with than any other breed - the length of time they lay is wholly determined by how fast they use them up. Leghorns probably don't fit the bill because although...
It would be good to have a general understanding of the laying life of a hen. A pullet is born with as many eggs as she'll ever lay. To make the numbers "even", let's say she is born with 1000 eggs in her. She can't make more, so once those 1000 eggs have been laid, she is done. Finito...