Great report - I've been wanting to go to Palau for years now. The Rock Islands just look amazing.
I'm interested that you got a bullet train to Mt Fuji - did this go to the mountain itself or just to a place with good views of it? I've been to Tokyo a couple of times but I didn't know you could do that. (I did get a great view of it from onboard our Osaka-Tokyo flight though - very cool.)