Here are some other Navy badges.
Extra-scarce Imperial Navy badge. This is the Navy Short-Term Commission Badge. From what I gather,
the Navy was desperate for skilled sailors, so they had a program that would bring in doctors, engineers,
etc to help for a 2-year period. They dangled the prize of only having to serve for two years, and then not
be drafted or called upon again. This badge was given to them upon completion of the service.

The program was quite limited and thus these badges are extremely hard to find. The quality is
exceptional. Made of silver with enameled ovals and stripes (appears to be stems and leaves), a nicely
pebbled background, and an attached blossom.

Peterson labels this the 'Badge for Army Service in the Navy' (pg. 94), but this appears to be incorrect. The
reverse of the badge and the box lid are inscribed 'Navy Short Service Completion Badge.' Another
Japanese source gives this English translation: 'Navy Short-term Commission Badge.'

Peterson also mentions a leather case. I haven't seen one, but there may be different kinds of cases.
(You can see this instance happen in the awarding of
Type II war wound badges, for example.) The
measurements given in Peterson's book are the same as this badge and box.

Another example is below.
Navy Marksmanship Badge
小銃射撃優等章
Shouju Shageki Yuutoushou
Instituted on September 8, 1911 (Meiji 44)
These may not be actual badges, but they were
awarded to students of the Naval Academy for
outstanding achievement. It is not clear whether these
were actually worn or just given as a prize.
The box is inscribed 'Award Badge.' 賞章
Shoushou
'Long Service, Yokosuka Navy Arsenal.'
'Long Service, Sasebo Navy Arsenal.'
2nd Class bronze
'10-Year Long Service, Kure Navy Arsenal.'
Imperial Navy Air Arsenal badge. The obverse has two characters that read 'Good Conduct.' The reverse says 'First Naval Air
Arsenal.' The original case reads 'Meritorious Labor Badge.'

The
Navy Air Technical Arsenal was located in Yokosuka. It was completed on April 1, 1932 and discontinued, of course, in
1945. The arsenal was involved in the design of aircraft as well as technical development of a number of other things related
to aircraft.

In 1940 the name was altered from that on the badge to the Naval Air Technical Arsenal, and again in 1945 to the First Naval
Air Technical Arsenal.

Since the 'First' on the reverse is stamped in while the other characters are raised, I am guessing that this badge was made
prior to 1940 and then awarded in 1945, with the new kanji added. The word 'technical' would have had to be put in the
middle of the old name, so that old name couldn't be changed.
Small badge: 'Long Service, Yokosuka Navy Arsenal.'
Large badge: 'Long Service, Toyokawa Navy Arsenal.'
'Long Service, Kure Navy Arsenal.'
Kure Naval District Race Prize. No date.
'Long Service, Yokosuka Naval Arsenal.'
1st Class silver-colored badge.
'Long Service, Yokosuka Naval Arsenal.'
3rd Class iron badge.
LEFT: 3rd Class iron badge.
RIGHT: 1st Class silver-colored badge.
Here are some naval arsenal long service badges. There were three classes of this badge, and they probably
related to the number of years worked at the arsenal. My written sources state that the 1st Class was
silver-colored, the 2nd Class bronze, and the 3rd Class iron. However, there are some gold-colored small
badges and bronze-colored larger badges. I'm unsure of why this is.

The official diameters are as follows: 1st Class 3.2 cm; 2nd Class 2.9 cm; and 3rd Class 2.4 cm.

The cases are inscribed 'Long Service Honor Badge.'
Naval arsenal badge?
'Passing Grade Commemorative Award, Navy Exam Company.'
Inscribed 'Good Conduct Commemorative, Naval Academy, Showa 11 [1936]
October.' The maker's label shows this was made in Hiroshima, which was
where the
Imperial Japanese Naval Academy was located.
'Prize, Kure Naval District, United Competition.' Pre-war badge.
'Made by Hinago Jitsuzou.'
An award from the Ministry of the Navy, dated Imperial Year
2600 [1940]. The wood plaque is in the shape of a traditional
Japanese shield, and the attached metal plate shows the
famous monument in Miyazaki then called the '
All the World
Under One Roof Tower.'

Inscribed on the case and plaque 'Imperial Year 2600
[1940], Ministry of the Navy, Naval Review Commemorative.'

The red ribbon says 'Made by Hinago Jitsuzou.' Hinago was
a famous sculptor (b.1892-d.1945) who designed many
medals as well as larger works like this monument.

This monument was unveiled in the same year as this
award is dated, so perhaps the naval review was conducted
in Miyazaki.

The plaque measures about 17 cm by 10.5 cm
The actual monument
Hinago designed.
This still stands in
Miyazaki City,
re-named the Peace
Tower. The wartime
inscription remains
intact.

Current photo.
1940 photo showing the unveiling
The monument shown on a 10-sen note.
Inscribed 'Navy Machinist Academy, Graduation Commemorative, 14th Cadet Class, Machinist Skills
Cadet.' And hand-engraved: 'Instructor.' (The Wikipedia page is only in Japanese.)

This academy of the Navy was only open for about 4 years, from April 1, 1941 to July 15, 1945. It was
located in Kurihama, Yokosuka.

I translated
kousaku as 'machinist,' but that word in English is a bit narrow. Cadets at this academy
learned everything from construction to damage control. Including but not restricted to forging, welding,
diving-related construction, fortification, etc.
'Large Naval Review, 35th Anniversary of the Battle of
Tsushima. Celebration 2600 [1940].'

This badge originally had an enamel Z flag in the center
rectangle on the obverse. This badge is missing that flag.
'Long Service, Maizuru Naval Arsenal.'
Other Navy Badges
Inscribed '3rd, Navy Ammunitions Arsenal.' Also inscribed
'good conduct' on obverse.

This arsenal was established in 1919 and was located in
Kanagawa Prefecture, Hiratsuka City. The '3rd' stamp most
likely refers to the arsenal section, of which there were
seven. This section was primarily concerned with the
production of acid, the collection of waste acid, and the
production of coal gas.
Also inscribed 'good conduct' on obverse.