I found the following info when snooping around the Library of Congress:

Jazz on the screen: a jazz and blues filmography by David Meeker
https://www.loc.gov/item/ihas.200028021/
(leads to this: )
http://memory.loc.gov/diglib/ihas/ht...reen-home.html

and

https://www.loc.gov/item/jots.200016017/
Specific information about H50.

It suggests that Broughton was music supervisor along with Don Ray, but this does not jibe with info at IMDb.

It also IDs two musicians who had speaking parts in S03E02, Trouble In Mind, which featured vocalist Nancy Wilson: Trummy Young (trombonist) and Red Callender (double bass). Young is the guy who tells Martin (Harry Guardino) that he can't play any quieter, and Callender is the one who tells Eadie that she is "the queen."

There is further information about musicians who were connected with the H50 soundtrack (I don't know if this specifically relates to Trouble In Mind):

Music Arranged by: Sammy Nestico

Soundtrack Personnel: Inc: Bobby Shew,Bob Findley, trumpet; Alan Kaplan, trombone; Vince DeRosa, Brian O'Connor, French horn; Terry Harrington, sax; Gene Cipriano, woodwinds; Howard Roberts, guitar; Max Bennett, acoustic double bass; Carol Kaye, electric bass; Chuck Rainey, acoustic double bass; John Guerin, drums; Larry Bunker, Emil Richards, Joe Porcaro, percussion.