While you wait for a more specific answer, my answer on Late Imperial China's interaction with Western colonial powers and missionaries, which includes some discussion of why Christianity was unable to spread effectively under the empire, can be found here, and /u/cdesmoulins discussed Jesuit missionaries in Early Modern Japan here. Additionally, /u/ivymikey (edit: and /u/dsk_oz) answered a similar question (with an emphasis on Korea) a year ago here, but a more Japan or China-focussed answer may still be forthcoming.

Addressing your comment about christian churches in the PNW (I assume that means "Pacific North West"), I think that might give you a skewed perception of the prevalence of christianity amongst koreans.

You might have already seen the linked thread where I discussed christianity and the korean diaspora but the gist of it is that korean churches serve as cultural gathering points for migrant koreans. New migrants moving to the US (or any other country) found themselves in an unfamiliar locale where everything was different. Many of the people joining churches might not even have been christian before migrating. Subsequent generations, e.g. born and raised in the US, would tend to be not as reliant on the church for their social and cultural activities.

Another factor to take into account is that korean protestant churches tend to be decentralised, i.e. many dispersed gatherings vs one large gathering. Depending on the size of the korean community in an area you might well see large gatherings, but it's far more common to see a small gathering renting the building of an existing church and doing their masses after the owning church has done theirs. It might well be that the PNW area has large gatherings that have evolved to owning or building their own places of worship but they would have all begun as the small gatherings that I mentioned.

Both of those factors would tend to make korean christian churches much more visible to the eye so that might give the understandable impression that koreans are invariably christian and christianity is dominant amongst koreans. That's not the case in korea itself, most people are areligious and competing religions like buddhism and catholicism are just as prominent. Protestantism definitely doesn't dominate the landscape.

But the title of your question does raise an interesting point. Why korea and nowhere else in asia?

The key to that lies in understanding why catholicism, the first type of christianity in korea, gained root. The first converts were learned scholars who read religious works translated into classical chinese (which they could read). Those scholars approached those texts as philosophical works, no different from confucian and neo-confucian works that they were already deeply familar with.

Another factor that I'd suggest is involved is the link between learning and morality in korean society. Basically a learned person is associated with being a moral person. This has long roots, with a typical image of morality being the image of a confucian scholar diligently working at his government post and going back to his poor dwelling at night. That image is that of an incorruptible man of learning who uses that learning for the betterment of his nation. Learning is a virtue in itself, rather than being a vehicle to personal gain of some sort, and gives a person a high social standing. Of course in practice it isn't always the case that morality necessarily follows learning but even today someone with a doctorate or an academic position is given a high social standing beyond any income that the position derives. That notion of the virtue of learning for the sake of learning would've made it easier to explore catholic texts.

Overall the academic climate in korea made it easy for a foreign philosophy to be examined and gain a foothold, with the result being that korea is the only country where no foreign preachers were involved in the spread of catholicism.