There are many flaws in your reasoning:
According to both player and AI test feedback, Japan too strong right now.
The AI feedback pointed out that Japan's performance is volatile with AI difficulty. Between Emperor and Warlord, Japan had the largest rank variation (3rd and 36th, respectively) among the civs, indicating that AI Japan's performance has more to do with its interactions with handicaps than with its kit. And, as far as I'm aware, human feedback has been varied on how strong Japan is.
Their playstyle facilitates clean transition between domination, culture and science victory focuses late game,
Only for high difficulty AI. Human players and lower difficulty AIs are not going to get the strong scientific conversion you're stating. The Dojo's yields on leveling mechanic scales exponentially and has a prior case of letting Japan get 10 techs or more ahead of everyone in Deity, but not in human hands, when Japan's UA was undergoing experimentation with it. I think you're greatly underestimating the gap that this mechanic has between human, AI and difficulty settings.
Bushido shouldn't be on boats
- Balance:
- This bonus is contributing Japan's power at sea. The Bushido promotion bonuses are better on boats than they are on land units
- Human players have reported making great use of it, especially in combination with Authority's 15 HP on kill. heal on kills is really good on boats, because they can't heal outside friendly lands normally.
- Fight better damaged is another thing that works really well on ships that can't heal anyways. If you can't heal up, you may as well hit harder
- Update history: This is the most recent buff given to Japan. Last hired, first fired. They were doing well before this, they certainly don't need it.
- Design overlap:
- This forces an overlap between Japan and Denmark. Denmark is the civ with bonuses to land/sea melee already.
- Imperialism also gives melee boats fight better damaged, and the two bonuses don't overlap. Japan's bonus partially overwrites a policy bonus
Bushido was already on boats back in BNW, with ships fighting at full strength when wounded, and early VP versions had Japanese melee boats also being able to set fishing boat improvements. This civ already had a long history of playing as a hybrid land/naval melee focused civ, and there's nothing wrong with reviving that theme. Especially if doing so connects an otherwise isolated part of the civ's design.
Denmark doesn't have a monopoly on it; they originally didn't have a bonus to any naval units in the first place. It was purely to embarked units, and melee units not having a movement cost to pillage. The addition of naval melee was on VP and both civs gravitated towards the melee land/naval focus, with variations from time to time.
Also, the warring style of both civs have very different focuses and don't share any mechanic; the only thing they share is the melee land/naval theme. This is not like the France/Japan discussion of both using the same 50% GWAM progress mechanic alongside the same cultural/militaristic hybrid theme, Denmark and Japan actually have no common mechanic between their kits.
Of note about Imperialism was how that bonus was suggested to be named "Banzai", in reference to Japan, after the bonus got changed from "Ironsides to naval units" to its current effect. If the overlap is a major issue, why not revert the policy back to giving Ironsides?
The Mongols chained their boats together to counter possible Japanese boarding actions, but that mainly made the storms worse. The Japanese can't take credit for that.
The Mongols had already felt how catastrophic a typhoon could be for their fleet in the first invasion, yet, they still opted to chain their fleet in the second invasion. They knew it could magnify their casualties in case of another typhoon. If they preferred to take risks with a typhoon over being boarded by the Japanese, then we have an indication that the latter was actually a major deal.
- Also cited was the Imjin War, and this is where the idea gets a bit silly. The Japanese were SLAUGHTERED because of their dependence on boarding actions in that war. They lost almost every naval engagement in that war against better-made Korean ships that emphasized cannons. In 1 engagement, the Japanese lost more than 200 vessels against 16 Korean Panokseon Frigates. The Koreans didn't lose a single ship. The Koreans created their own anti-boarding ship, which is a UU in the game already: The Turtle ship. These ships completely countered the Japanese. The Koreans never lost a single battle where a Turtle Ship was engaged, and they didn't lose a single one in the entire war. The Imjin war can be summed up as follows: Japan invades and quickly wins the land war and conquers all of Korea, but then fails to protect their ocean supply lines, causing their occupation to collapse against partisans and guerilla remnants. And we want to highlight this atrocious failure as a UB ability? How is a historic naval humiliation supposed to be the basis for a bonus?
- The Japanese naval presence was not normally composed of warrior-poet bushido-following Samurai boat boys. They were a rabble; thieves and peasants with rowboats and guns. Oda Nobunaga's "Admiral" was a pirate. Japan only professionalized its navy with the Meiji reforms in the 19th century, and they won their greatest victories with long distance shelling. Ranged Naval. And after that they were at the forefront of the Aircraft Carrier revolution. Their preceding time spent depending on naval melee engagements were marked by Japan's amateurism, defeat, disgrace, and isolation.
- Japanese shipbuilding was awful. Half the reason the Japanese were so dependent on boarding actions was because their ships were so flimsy they couldn't handle the weight or recoil of cannons. They build massive floating fortresses called Atakebune, and they weren't seaworthy at all. Then for the next 300 years, building large combat-worthy ships was outright banned by the Bakufu.
You're greatly downplaying the importance of Yi Sun-sin in the war.
The most notable counter to your argument is the Battle of Chilcheollyang. At the time, the Korean king was of the same opinion as you that the Japanese fleet was more of a rabble and became distraught when Yi refused to obey the king's orders to attack. Yi's refusal was based on tactical concerns, but his insubordination nonetheless led to the king ordering Yi to be imprisoned, tortured and almost executed. Meanwhile, the whole Korean fleet was to be commanded by Won Gyun, who obeyed the order. Despite having the same ships and personnel as Yi had, commanding the fleet at the height of its strength and already having fought alongside Yi in this war, he suffered a crushing defeat; from up to 200 ships, only 12 or 13 survived due to them fleeing just before the battle began. The rest of the Korean fleet was quickly approached, boarded and slaughtered by the Japanese fleet, with the Koreans not getting a chance to fire their cannons. Meanwhile, the Japanese suffered minimal losses. There, the Koreans lost proportionally far more of their fleet (near total annihilation) in a single battle than what the Japanese lost over the entire war.
This defeat served as a reality check for the Korean court, and later historians, of the strength of the two fleets. The naval technology the Koreans possessed proved to be neither decisive nor dominant, and the Japanese fleet proved to be a formidable threat on its own right, and actually advantaged over the Korean fleet. In the end, the core factor behind the Korean victories is attributed entirely to Yi's genius; the king recognized that and quickly reinstated Yi back after hearing news of the defeat, despite just nearly executing him.
Also, unlike what you stated, the Korean lost all their Turtle Ships in this battle, with those being unable to inflict any serious casualty to the Japanese ships. Without Yi's command, even the ship that specialized at countering the Japanese tactics was sunk without accomplishing anything in this battle.
Of note is that Yi would only allow melee confrontations against a Japanese ship if it was severely damaged. He understood well that the successes of the samurai at land were reflective of how dangerous they can be in a melee confrontation at sea, and tailored his tactics specifically to prevent that. This insight is what the bonus on melee ships is based on.
and 
to all military training and defensive buildings
CS bonus when defending (20% iirc), it changed at some point to give Tenacity (fight with additional strength when wounded) to ships instead. I was referring to change back to that promotion.
