Okay, I know these are old posts, but I hadn't seen this thread before, and I needed to respond to this:
This doesn't make any sense. Taking the introduction of firearms as the start of Japan's westernization process and the Boshin War as the end of it, and saying that because it took them three hundred years it should be a similar length in-game, makes it seem as though you believe they were spending all that time westernizing. As though Oda Nobunaga clicked the "Westernize" button, the Tokugawa spent the entirety of their tenure working on it, and it was finally completed during Meiji's reign. This, of course, is not remotely what happened. Oda (who was a daimyo, not the ruler of Japan itself) implemented some modernization of his military. After he was assassinated and Japan unified by others, the Tokugawa Shogunate, having come into power over Japan itself, abandoned all attempts at a modernization program. The 250-odd years of relative stagnation under them were not because westernization is hard; it was because they weren't even attempting it then. The Tokugawa closed off trade with outsiders apart from a few select ports for a few select trading partners, and what knowledge leaked in from those ports was certainly no more than any other non-westernizing power would have been receiving merely from trading with Europe. It was not a sign of a continuing westernization program. Japan made no further attempts to westernize until the Meiji Emperor came to power, and once they did, it only took a few decades.
It's impossible to know how far Oda Nobunaga would have taken things if he had survived and become shogun, but if Japan had a systematic attempt at westernization under him it would not have taken anything like three centuries to complete. Japan in the 1500s was simply not that far behind. If you want to put it that way, Nobunaga clicked "Westernize" as daimyo of Oda, his efforts were erased when Oda got absorbed, and Japan under the Tokugawa dynasty never clicked "Westernize". It wasn't until Meiji clicked it as ruler of Japan itself that the process got started, after which it happened pretty quickly. So to say, "Oh, Japan imported European firearms in the 1500s, but they didn't become fully westernized until the 1800s, so it took them 300 years, so it should take centuries to complete in-game as well" completely ignores the realities of what was going on in Japan in the interim. You can't take a country that abandoned all efforts at westernization for two and a half centuries and argue that a country in-game that is actively trying to westernize should have to take as long as they did, or even two-thirds as long, because their experience shows how slow westernization is. For nearly the entire period you're talking about, they weren't even trying to westernize, so you absolutely cannot count that era as part of how long westernization took them.