It might be of interest to check the radio page of Mudcat. There is archived there an interview I did with David Margolich who wrote the book "Strange Fruit". I think you will find his insights into the song quite interesting. Also his comments of Holiday vis a vis White, as wel as his comments on the authorship (you are right---it was not a triumvirate). It was Abel Meerapol alone.
He also relates a wonderful story of Holiday's confrontation with White about the song---and how she did not really get it at first(the song)---then took it as her own and created her legend of being involved with witnessing a lynching--never happened.
Better yet---read the book---it is truly interesting and well written by this contributor to Vanity Fair, the New York Times and other publications.
You might also check out Ron Olesko's interviews with Elijah Wald (biographer of Josh White) on the Radio archives of this website.