And, well, it turns out that the Japanese adopted the Gregorian calendar in 1873 during the Meiji Restoration, which is what I was thinking was probably the case.
But here's the freaky bit. I just noticed that the Japanese and Latin days of the week are the exactly the same. Three modern English weekdays are the same as Latin, the rest are German or Norse:
Monday: Moon Day [same in most European languages, Romance or otherwise]
Tuesday: Tyr's Day [German god of war, lines up with Roman Mars]
Wednesday: Wodin's Day [Norse -- doesn't really line up with anything Roman]
Thursday: Thor's Day [Norse -- Thunder to go with Roman Jupiter's lightning]
Friday: Freya's Day [Norse -- or possibly Friga/Frigg's day, those are German/Norse goddesses of beauty like Roman Venus]
Saturday: Saturn Day [Roman]
Sunday: Sun Day [Roman, same in most European languages]
But in Japanese (Roman weekdays):
Mon: 月曜日 (getsuyoubi/moon day) - 月 (tsuki/Moon) - Moon Day
Tue: 火曜日 (kayoubi/fire day) - 火星 (kasei/fire star/Mars) - Mars Day
Wed: 水曜日 (suiyoubi/water day) - 水星 (suisei/water star/Mercury) - Mercury Day
Thu: 木曜日 (mokuyoubi/wood day) - 木星 (mokusei/wood star/Jupiter) - Jupiter Day
Fri: 金曜日 (kinyoubi/gold day) - 金星 (kinsei/gold star/Venus) - Venus Day
Sat: 土曜日 (doyoubi/earth day) - 土星 (dosei/earth star/Saturn) - Saturn Day
Sun: 日曜日 (nichiyoubi/sun day) - 日 (hi/Sun) - Sun Day
Which matches up exactly with the Roman days. Hindi and Korean apparently do as well (but not Chinese, which uses numbered days, which is another common pattern, even in Europe).
And I just noticed that, because the only planet name I knew in Japanese was Saturn, and the connection didn't occur to me (I'd long since noticed that Monday and Sunday matched up, but figured that could just be coincidence and got lined up when they synchronized calendars). I guess now it's pretty easy to remember the Japanese planet names, since I already know the days of the week (for an additional weird connection, think Mercury -> water planet -> fluid metal -> mercury, which probably isn't coincidence, either. And in Europe, that connection is older than any real contact with East Asia, so...)
Of course, I'm curious as to how it happened. Were the days of the week in Japan adopted from the west? Did it happen during the Meiji Restoration? Or during earlier contact? A lot of these changes followed Christian missionaries around the globe -- but the Portuguese, who sent the first missionaries to Japan don't use planetary days of the week, they use numbered days. On the other hand, they were bringing Latin with them, and presumably would have been teaching Latin to the converted so they could understand mass... But what about the planets? Do they have traditional Japanese names and changed to match the days, or vice-versa? And how to explain Mercury as the water planet, like the water metal? I suppose it's possible to rationalize, but it's still an interesting coincidence: Mars is red (fire -- okay, pretty obvious), Mercury is fastest (like water, if you need to pick a Chinese element, that makes most sense, which is apparently where the planet or weekday names came from, whichever came first), Jupiter for wood (uh, okay, whatever), Saturn for earth or soil (uh, okay, whatever), Venus for gold (it is pretty bright, and a bit on the yellow side when low in the sky).
I guess the planets probably came first, if I was going to guess, Jupiter and Saturn don't really match up very well to anything in the west that I can see without getting unlikely and obscure.
Unfortunately, I haven't been able to find out all that much yet. But I'm very, very curious.