Overall it's a solid plan. Although you have to prepare for things not going exactly according to plan, it's always good to have a list of the things you'll want to see and do, and you've definitely done your research.

Two suggestions:
- Make sure to get to Kurama-dera early (it opens at 6AM, IIRC.) You'll (almost) have the place to yourself as you do the hike to Kibune. And when you finish your walk, perhaps have lunch at HIrobun, which offers the Kawadoko experience until about Mid-October.
- If you're wanting to see Fuji, it's best viewed early in the morning (if it's not covered in clouds, which is always possible.) Given that, I'd suggest that you go from Hiroshima to Kawaguchi-ko, and stay overnight at a hotel or ryokan there. Or, alternative, head over to Hakone, and you might have a chance to see Fuji from either Ashinoko (Lake Ashi) or the Owakudani area. From there, spend the rest of your time at Aman Tokyo.

Agree with 1200GS that Miyajima is an amazing place. But you need to spend the night to truly get a sense of the magic, after the hordes of daytrippers have left for the day (and before they arrive the following morning.)