First, the group Onmyouza. They actually do exactly what I was looking for: Traditional Japanese musical motifs with a metal sound. Plus, they perform in costumes based off of traditional Japanese clothing. (Hot!)
Second, Matenrou Opera. ("Matenrou" means "skyscraper".) Musically these guys are all over the board. Some of their stuff is very, very metal. Some of it is bordering on pop idol music. A lot of it is solidly what I would usually call "visual kei".
That last bit led me to realize that what I think of as "symphonic metal" is frequently expressed in the visual kei genre in Japan. The unfortunate thing is that I think an awful lot of the visual kei bands put an emphasis on form over substance, which means the musicality suffers. The two groups I mentioned above I was impressed with their musicality.
I also realized that X Japan counts as symphonic metal. Huh.
And lastly, I found several metal groups with female artists who have a metal sound, but lay Japanese girl idol pop voices over it. I find this very, very jarring, and will avoid that.