That doesn't look unmanageable, but it will be an active holiday. Assume you will be doing the two week railpass?
Personally I would consider dropping Hakone and consider somewhere smaller for the room with private rotenburo - but that might just be because I found Hakone a bit commercial.
I'd even consider whether you really need Osaka as well as Tokyo. I'd consider a visit to Himeji castle and or Naoshima (if art / architecture are of interest).
While we lived in Japan we did a week's honeymoon doing the following:
Tokyo
Kyoto (Ryokan Tawaraya)
Nara
Kanazawa (Gardens and Pritzger prize winning art gallery)
Shinagawa-go (Thatched houses in a valley)
Hida-Takayama (visit town, Hida folk village, and stay at Ryokan WanoSato a taxi-ride outside town)
Tokyo
Also just back from a two week trip to Japan where we did (a busy trip) that included:
Tokyo
Shikoku
Naoshima Island (Art / Architecture)
Kyoto (Kikusui Ryokan near Nanzenji)
Amanohashidate (a scenic view probably not worth the journey)
Tottori
Matsue (castle, Lafcadio Hearn, Samurai house and Adachi Museum of Art - gardens)
Arifukuonsen (Nushiya Ryokan - best ryokan in Shimane - recommended if you are anywhere near)
Kyoto (AirBnB traditional house just South of Kyoto Station)
Tokyo
Found the much less travelled West / northern coast of Honshu a good trip, through definitely benefitted from having a friend with a car as tour guide from Amanohashidate to Tottori via Ine and a fantastic lunch at Mitaki-en near Chizu.
If you do go to Hiroshima and Miya-jima I would recommend staying on the island as then you get to see it without as many tourists.
In Kyoto, we would probably recommend the ryokan we stayed at this time - near Nanzenji shrine over Tawaraya - which might be a 'grand dame' but is probably less good on a cost/performance basis.
Early October will still be quite warm in the day, but do pack layers.
Happy for you to PM me if you would like to ask questions about any of the above.