Tod Sloan's riding career was 1893-1900. "...George M. Cohen coined Sloan's most famous nickname, Yankee Doodle Dandy, written about the American Jockey."

http://hall.racingmuseum.org/jockey.asp?ID=222

In 1899, Manuel won the Kentucky Derby, Fred Taral was the jockey. Fred Taral's riding years were 1883-1908.

A quick search on the net didn't locate any jockeys named Bergen or Hamilton.