Definitely pick up the book. It starts out with a dialogue between Mingus and the psychiatrist who wrote the Black Saint liner notes, and briefly delves into the whole Jewish thing. Gets a little erratic in other places, but overall, worth the insight at least.

I’m with you on klezmer, which does have that same streak of improvisation, not to mention a harmonic sensibility outside of the European mainstream. It’s a big part, but I also think it’s significant that Jewish and Italian immigrants were unloved by American society and, for a time, not even considered white. So when you consider that sociological reality in light of their preexisting musical aptitude, perhaps the jazz thing isn’t so surprising.