I don't think that our Fredericks can be the same, but I wouldn't be surprised if there is some connection. I have Frederick's birth certificate--he was born on July 25, 1873 in NYC. He was my father's grandfather and my father knew him all his life. He never moved from the NYC area.
I know from this birth certificate that his parents' names were Johann and Sophie Dankert. Sophie's maiden name was Kretzmer.
I do have a letter from Johann's brother in Germany and there is reference to a Carl (which would be Charles here) who moved to Chicago. He was a carpenter. My gggrandfather Johann was also a carpenter.
The letter also mentions a Marie Dankert who lives in Chicago (apparently not married to the Carl). She was a dressmaker. These are the only midwest connections that I know of.
I wouldn't be surprised if my John and your Frederick were brothers, or some relation. From the letter I have, it sounds to me like the family tried to keep in touch, despite the long distances.