RE: Harry Byrd was an independent.
Not according to Wikipedia:
Born Harry Flood Byrd
June 10, 1887
Martinsburg, West Virginia, U.S.
Died October 20, 1966 (aged 79)
Berryville, Virginia, U.S.
Political party Democratic
Spouse(s) Anne Douglas Beverley
Children Harry F. Byrd, Jr.
Religion Episcopalian
My bad...I was referring to his son, Harry Jr.. They were both Senators from VA. But both were pretty darn conservative.