Following my initial post, below is a summary of replies and suggestions with references dealing with the history of hearing science.
First, here are references to works written by people who have been active in hearing science (psychoacoustics,anatomy/physiology, physics/acoustics, engineering/signal processing, cognitive psychology, audiology).
A brief historical overview of psychoacoustics recently published by Bill Yost in Acoustics Today
It contains a reference to the classical reference to Boring's work that treats hearing at length, along with other modalities, though only up to 1940s. (Boring, E. G. (1942). Sensation and Perception in the History of Experimental Psychology. Appleton-Century-Croft, New York.)
A useful perspective on the history of hearing science, with strengths and shortfalls, can be found in Reiner Plomp's book (Plomp, Reinier. The Intelligent Ear: On the Nature of Sound Perception. Mahwah, N.J.: Lawrence Erlbaum Associates, 2002.)
F. V. Hunt's Origins of Acoustics (Published in 1992; Originally Published in 1966). "..covers the history of acoustics from the ancient Greeks till the end of the 18th century. "
Robert Beyer "Sounds of Our Times. Two Hundred Years of Acoustics" (published in 1999). "Beyer separated the 20th century development to sub-disciplines, where it could be easier to single out the highlights related only to psychoacoustics, the physiology of the ear, etc."
Other detailed historical accounts written by practitioners of hearing science, giving a sense of historical and personal context can be found in
S.S. Stevens' autobiographic chapter Notes for A Life Story. Being recollections assembled in no particular order for a volume History of Psychology in Autobiography, December 1970 http://link.springer.com/chapter/10.1007%2F978-94-010-2245-3_41
(the description of war time studies on the effects of noise exposure and the descriiption of Stevens and Newman clearing up the collection of human brains dating back to William James are quite vivid).
The ASA collection of Fletcher's papers, edited by Jont Allen (ASA EDITION OF SPEECH AND HEARING IN COMMUNICATION. Harvey Fletcher; Jont B. Allen, Ed. Summary of Harvey Fletcher’s 33 years of acoustics work at Bell Labs. (A new introduction, index, and complete bibliography of Fletcher’s work are important additions to this classic volume. 487 pp, hardcover 1995 originally published 1953)
Davis, Audrey B., and Uta C. Merzbach. Early Auditory Studies: Activities in the Psychology Laboratories of American Universities. Washington: Smithsonian Institution Press, 1975. https://repository.si.edu/bitstream/handle/10088/2430/SSHT-0031_Lo_res.pdf?sequence=2&isAllowed=y
Davis, Hallowell. “Psychological and Physiological Acoustics: 1920-1942.” Journal of the Acoustical Society of America 61, no. 2 (1977): 264-66.
In addition, several replies pointed to a vibrant literature that deals with the history of hearing science within broader cultural, musicological, sociological, philosophical perspectives.
Alexandra Hui's "The Psychophysical Ear. Musical Experiments, Experimental Sounds, 1840-1910", published by MIT Press in 2012:
Lisabeth Fauble wrote “The first chapter of my book, Music Therapy: Understanding the Science of Sound delves directly into the emergence of human understanding of tone, pitch and dynamics beginning in the neanderthal age. This book draws directly on my own graduate research studies and incorporates theories from renowned acoustical scholars and neuroscientists like Steven Mithen, Daniel Levitin, Robert Zatorre and Ani Patel, among others. A lengthy excerpt of the first chapter of the book is available for free review, so you can determine if it's something you could use for your graduate level course.”
"Alistair Isaac is writing interesting papers about the history and philosophy of psychophysics, focusing on colour and timbre:
Thanks to all who replied: Bill Yost, Dick Lyon, Marcin Wroblewksi, Seth Ayyaz, Philipp Aichinger, James Johnston, Christopher Haworth, Adam Weisser, Roland Wittje, Mary Rudner, Diana Deutsch, Lisabeth Fauble.
There is plenty of good reading in these references. Although none seems to provide a comprehensive history of hearing science, especially for the second half of the 20th century up to the present, clearly such history is in the making.