A good summary, but you have some typos and an error for the five AA Directors installed on USS WASHINGTON.
You have typos calling all the directors as "Mk 37", which only the four 5-in gun DP Directors were. The main gun directors were Mk 38/40.
The five AA Directors onboard were Mk 45 not Mk 42. The Mk 45 and Mk 49 directors were being developed in parallel at the same time. The Mk 45 director was much larger with two operators and rangefinder installed, was intended for use on large ships like battleships (and even USS TERROR). Only 51 were built when production was cancelled in September 1942, after it was found to be a failure. The Mk 49 directors was intended for smaller ships with one operator and no rangefinder (range-only radars were installed on some late built units) and as supplements on larger ships. The Mk 49 director project after much trouble (primarily slow servos) and failed upgrades was also cancelled in September 1943, after some 343 units were built of various marks.
A good photo of the Mk 45 director is attached.
The USS Washington had some noticeable differences from her sister, even in late 1942. The following notes are based on her August 1942 appearance as there are several Hi-Res images of her completing her refit before sailing for the pacific, so smaller fittings such as additional 20mm or even .50cal guns could easily be added by repair ships in forward bases by time she hits her famous November battle but major structures seem to remain through her refit in early 1943.
Her AA-
I made this infographic laid over a later war drawing. This is based on the images taken between 8/18/42 and 8/21/42. There is a famous photo allegedly taken during the night action with Kirishima and it shows a trio of 20mm's on starboard side forward of #1 Turret in the open. I believe this image to be inaccurately dated based on what I believe to be a MK8 radar mounted on her MK37 gun director which would not be installed until 1943. I could be wrong as the picture is unclear and there are few clear points of reference. They are absent in a photo dated a couple of weeks late on 9/1/1942. These 20mm's could easily have been added after her arrival in the Pacific, so plausible but my gut tells me not likely. Interestingly, it appears that the Washington sailed with 5 MK42(very similar to the later MK49) Gun directors for her 1.1's and a single MK51.
Other differences of note-
Washington had fewer Portholes in the Pilothouse vs North Carolina
There is a support brace that runs along the Centerline from the base of the FWD MK37 to the face of the Director Tower
The one on the aft MK37 tower is more integrated into the aft structure with openings in it.
The aft MK37 (Sky 4) has a raised MK4 Fire Control Radar
The MK37's had the 6'X6' version of the MK3 Fire Control Radar mounted on arms that angled back
SG Radar was mounted on the face of the Control Tower(This caused the famous "Blackout Zone" during the night engagement)
As noted already, Washington never was fitted with the "Stryker's" Bridge platform around the FWD Control Tower
The area above the Pilot house would be different from how Trumpeter did it for a 1944 North Carolina, it was a more squared off open bridge with wind venturi
There was note of the height and location of some of the Twin 5/38's being incorrect on the Trumpeter kits, but I do not have those at hand right now to double check.
Kraken Hobbies makes many of the fittings to backdate a Trumpeter North Carolina to the Washington of late 1942. We have a few that are not in the shop currently pending final print checks need to occur, but feel free to reach out if interested.
1/350 USS Washington Parts
Model Monkey also makes fantastic 16/45 Turrets, 5/38 and correct funnels.
Model Monkey
Hope this helps,
Matt
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USS North Carolina? Certainly omit the "platform" on the control tower structure but what else?