Hello there,
I am no expert on the American Champs as living in London I have no access to original sources. I am seeking to complete the same "table" for the American Champs as I have done for the English ones and this is difficult.
However I do have a birth of a Joseph Columbus Champ on 14 May 1875 to Jackson Daniel and Mary Ann (Bailey). He was born 24 Feb 1844 to Nimrod and Rachel (Skidmore) and there are many references on the net to this couple and Nimrod's forebears. I think you are right about your descent from the Sgt Major John Champ and I think he comes from the Champs who arrived in Virginia in the 1620's. I would assume they came from England as VA was an English settlement then but I do not know enough of American history to be sure.
There are several sights. I have found lots of information just searching for "Champ" but this produces lists of boxing champs as well! so you get alot of rubbish included.
Have you tried the Champ page on Family Search. R J Ballantyne seems to be the expert on the American Champs but he is not the only one interested in the name by any means.
Any information you can provide, particularly your brother's sisters etc is always appreciated. Going by Jackson Daniel's age, your father must have been one of the younger members of the family.
Good luck with your search. Please let me know how you get on.
Lewis Sale
London UK