The result would be fully Orthodox, but architecturally and aesthetically styled based on Japanese capabilities.
What you think that there is something un-Japanese in normal Byzantine rite Orthodox traditions? Western people seem to have some strange idea that non-White people are unable to comprehend regular Christian traditions. That's weird since there is hardly anything specifically Western or White in Christianity.
Pardon for ranting. Not specifically directed at you. I'm just sometimes bewildered over some ideas about how to adapt Christianity to non-Christian cultures.
Certainly not. The enthusiasm with which the Japanese and many other cultures have embraced the beauty of Byzantine and Slavonic liturgy, music and architecture proves that as a form of worship the Easrern rites are able to transcend cultural barriers, perhaps with even greater dexterity than the old Latin Rite of the Roman Church, which as a rule did not make any provisions for acculturation.
Rather, as an aficionado of Japanese artwork, gardens and architecture, I would like to see the Japanese Orthodox build Orthodox temples and paint icons in such a way as to represent a distinctly Japanese cultural expression of the Orthodox faith.
I get what you're saying. The Russians/Slavs made the Byzantine style "their own", including a lot of native elements and building upon it rather than just taking it as it was. This was a process that took a long time. Take for example this, which would have been beyond the original Byzantines' wildest dreams:
The Japanese could further develop the Russian style. St. Basil's, coincidentally enough, rather resembles a lot of Japanese architecture already. If you made the spires and onion-domes a bit longer, changed them to be something like a squircle
in cross section, and added sloped roofs at regular intervals, you'd have what looked like a church made of pagodas (Japanese pagodas are square and most of their architecture is rectilinear, but Orthodox symbolism uses circles more often, so rounded squares could be used). The color scheme is another area where a lot of localization is possible (St. Basil's itself got its own colors over several centuries). It'd be both recognizably Japanese and
recognizably Orthodox at the same time, and while not strictly Byzantine (any more than St. Basil's is), those roots would also be apparent. Symbolically it'd represent the faith going from Byzantium through Russia to Japan. You'd also be paying homage to some of the earliest Christian churches in the region (which are believed to have been modeled on pagodas, with some alterations).
However the Japanese Orthodox Church would need to get a lot bigger before it can afford to build something on the scale of St. Basil's. Even small chapels, though, could be built in on similar principles, just, you know, smaller.