My wife is Japanese, born and raised in Japan, and spent most of her life in Japan before she moved to the states. When we watched this movie together a few months back, she found it to be pretty unusual, particularly the parts with the stones containing the souls and also the souls of the dead inside Godzilla. So this is not a "Japanese" thing, but this is more of a "Kaneko" thing. And at the same time, she loved Gamera 1 and 2 but felt Gamera 3 was also a bit unusual for the same reasons as GMK.
For me, I love GMK for what it is, an enjoyable movie with a complete baddass Godzilla. I love the FX, battles and the destruction, but I really don't care for the unusual spiritual tones of the movie, same as Gamera 3. So from what my wife tells me, the spiritual tones of these two movies are not really Japanese, so if anyone feels that we don't understand them because we are not Japanese is not true at all. My guess is that many Japanese would feel the same as we do, because an unusual movie is an unusual movie no matter what country you're from