RE: Sandwich book
Cheese Frenchie is definitely a Nebraska sandwich...
But, though there's a great deal of debate, there's been a lot of research as well into the origin of the Reuben (credited in your book as New York's sandwich) - and the research leans towards a Nebraska origin of the Reuben as well.
I always thought the Reuben originated in Omaha - but according to the research, the earliest documentation of the Reuben in existence appears to come from the Cornhusker Hotel, in Lincoln, NE.
Just some interesting info.