It seems like Japan was exceptional in the way it sought to rapidly industrialize and adopt western values. Was this actually the case? If so, what made Japanese culture capable of doing so while so many other native cultures remained insular up until colonization?
It had very little to do with Japanese culture, and there were significant resistance to modernization in Japan.
What Japan had that most other states did not have in 1866 were
A comparatively high level of development: Japan's level of development was much, much higher than say, the Aztec empire in 1500. What this meant was that Japan had a smaller gap to close between itself and the west.
More importantly, unlike almost every other state which attempted modernization before the 20th century, Japan had a strong and functional state in the 19th century. Under the Tokugawa Shogunate a strong government was created at the center and a strong bureaucracy was created through the process of hiring Samurais into government service as bureaucrats and tax collectors. This had the twin advantage of creating a strong tax base, an efficient state, as well as to get rid of a huge source of instability (Samurais) in the countryside.
What this meant was that when Japanese government wanted to modernize, they had the means to do it. Once a capable group of political elite takes control a strong, centralized state is capable of overriding the opposition, using deadly force if necessary. Not only that but a strong tax system meant the government actually had the resources (money) to do it. It also gave the government means to setup additional institutions (i.e army, naval academies) to complement existing ones.
Compare Japan with neighboring China, which attempted to do the same thing as Japan, and was a failure by comparison. Despite importing western technology, expertise and hardware, China failed to develop a modern nation by the early 1900s. This was not for the lack of trying, it had to do with ineffective state institutions in China and efficient state institutions in Japan. In many ways China manage to import the "hardware" of modernization without the "software" to run it.
One of the great lessons of developmental economics, not just in the 1860s but all the way up to today, is that institutions, not culture, population or even natural resources is the key determiner factor.It's whether states are able to build effective institutions to make use of the fruits of modernization. This is often difficult as it destroys the power of pre-existing elites. The general failure of development even in the second half of the 20th century in Africa and the Middle East can be traced to failure to develop effective institutions more than anything else.