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Lynn it has been my experience that the only good layers of the game type birds are the Old English. If you do breed to a Cornish, OE or many other breeds it will set the tail carriage way too far up and it will take years to get it back down like it should be if ever at all. You can see that in the Sumatras at the shows now. I imagine that breeders crossed a few of them with longtails to get a fuller, longer tail and now the males hold it way too high. A Sumatra, Yokohama and Cubalaya should have a straight line from the base of the neck to the tip of the tail.
Now a natural way to increase the egg volume would be to use a trap system on the laying nests so you can record which hen layed the most eggs then breed from her and her offspring, only keeping the highest performing layers. It will take a little longer to get to where you want to be but you will be able to keep the breed intact.