Phil, thanks for posting the report and the pictures! You're lucky to just be in Japan, for the opportunity. I'll definitely try to do that hike if I am ever in Japan (which is not likely to happen).
Your description reminds me a little of hiking Mt Lassen in northern Calif. It is also a volcano, but certainly even easier than Mt. Fuji. I hiked Mt Lassen in 4 hours (round trip!). But it definitely gives you the flavor if hiking a volcano.
...so when IS the "high season" for Mt. Fuji?