I can't see how "Beatles,Stones,Zepplin" qualify as "the most influential American musician of all time".
And Bela Bartok was almost 59 when he moved to New York, which he reportedly found "alien". Well, Stravinsky was about the same age when he arrived, but then again, he became a US citizen and lived in the US for another 30 years; unlike poor Bela, who died aged 64.
You are right about the list though.
Is the book you recommend "Louis Armstrong: An Extravagant Life" by Laurence Bergreen?
Regards,