Phil,
I have a copy of the "unpublished" OFFICIAL HISTORY "
U.S. Navy bureau of Ordnance in World War II" as well, it has been helpful to me to understanding the development, production, and installation of the USN weapons in WWII, particularly the 20-mm and 40-mm guns. The USA got manufacturing rights both guns, but had already been "back-engineering" them because the European versions required a lot of old-fashion "filing to fit" which resulted in no interchangeable parts. Legal use aside, the USA would have gone ahead and built the weapons anyway. Also, I have been going through the King Board Air Defense Improvement Program files at NARA. The development of the weapons was one thing, but the actual installation onboard ships took a lot of effort as well. It was interesting how much effort went into figuring out the "tub" bulwarks, etc with early production (prototype) twin and quad 40-mm mounts. The one area that the Official History didn't cover was the development of the Fire Control necessary to use the 40-mm guns. The guns were ready and in production as you say in the Spring of 1942 (behind the original predictions and plans for installation in new construction and refit to older ships), but held-up for lack of an adequate FC system. The Mk 51 using the "electronic" Mk 14 gunsight developed for use on 20-mm guns, was a crash interim program when the Mk 45 and Mk 49 directors fell way behind in development. Ironically the "interim" Mk 51 director outlived the planned "ultimate" GFCS.
As with any new weapon, the first units to get the weapons were those necessary to TRAIN the Fleet Gunners. Shore-base and sea-based. USS WYOMING wasn't a Combat Unit during WWII, but she evaluated new weapons and trained 1,000's of crewmen in their use. From the photo dated on 26 June 1942 ...
https://www.navsource.org/archives/04/050/0405006.jpg (and at NHC) ... USS HELENA already had her quad 40-mm mount(s) installed by then. I came across a pair of images of USS HELENA in the background of USS SHAW (DD-373) as both were completing their "post-Pearl Harbor Attack" repairs. I had ignored this 2 July 1942 image because of the steam masking much of USS HELENA, but in going back and looking, the midships starboard quad 40-mm mount is plain to see.
OH ... One more thing. Getting ANYTHING from the National Archives is limited to what is available on-line for now. I and others have been in contact with Holly on the 5th floor (photographic collection) and she says she has not been in the College Park building nor seen her co-workers since the "lockdown" started. She works from home and "tries" to answer what she can to requests with what she can download from NARA's website. NARA stopped making Microfilm to Microfilm copies sometime ago. The making of digital copies to DVD (or a SSD or flash-drive) is something one has to contract for from a "for hire research" vendor. Suppose if YOU had the proper equipment, you could be allowed to do it yourself. Either way it will not be cheap. If you only need certain views, you can go in person (when NARA opens) and use either an "OLD and prone to breaking down" microfilm reader to make paper copies or use one of their new machines that makes digital copies to a flash-drive. I have used the new machine and it is a bit time consuming, but the quality over the paper copies is much better. However, they charge if I remember right $0.50 a copy. But, in my case I could go through multiple reels and just copy what I wanted (cropping excess margins as well), saving getting copies of 1,000's of gears and brackets.