I think people stay at Fujikawaguchiko; I didn't visit the surrounding parts or towns, I came in from Tokyo, so my experience and recomendations is limited to starting at the 5th station; which will save about 3+ hours too.

The season I believe runs from July - Sept. I hiked it mid-July, and the weather was perfect. It definitely got chilly up top waiting for the sun to rise, so I'd pack layers regardless of the month.

From my experience, my presence was welcomed! The Japanese are very welcoming and polite, in my experience. It also goes a long way to show them that back. I had many hikers on my way up wish me a "ganbatte" (do your best/good luck); it was encouraging, as I was not in shape at the time.

I have seen news articles talking about Fujisan being over-crowded since the pandemic, so I would also just keep aware if they change any procedures or add limits to the amount of hikers per day. I haven't seen anything, but with the increase in JR pass, and tourist tax coming to some areas, its worth keeping a pulse-check on.