Gitler (both Jazz Masters Of The Forties and the oral history From Swing To Bop) and Deveaux would be my recommendations. Peripherally related, there’s Arnold Shaw’s 52nd Street (originally published as The Street That Never Slept, and which may be more 1930s oriented—can’t recall, been a long time since I read it) and Honkers And Shouters, which covers the rise of R & B and jump blues from a national perspective. Robin D.G. Kelley’s Monk biography gives a good portrait of the NYC scene during this time.
Throwing this in as an extra, because it’s not really music-related—but I also greatly enjoyed Victory City: A History Of New York And New Yorkers During World War II.