[allhailhata]

FYI,You need reserved ticket to Ghibli museum.
I don't know where will you stay in Tokyo.
But I think
"Tokyo day 3 Shinjuku + Shibuya" + Ghibli museum in Mitaka is the best choice.

19 Kyoto City sightseeing
20 Himeji + Miyajima 1 day tour
21 Fukuoka.

Going back to Kyoto after Miyajima is not efficient and not usual.
Staying Hiroshima or Miyajima is normal.
If you like Ponyo,I recommend Tomonoura in Hiroshima prefecture.

24 not decided yet
25 not decided yet
26 not decided yet
27 Tokyo check in

On the way back to Tokyo,I recommend Kobe,Osaka,Kouyasan and Fuji.
If you don't mind long train ride,Tōhoku region is another choice.

Btw,according to your itinerary,you are going to visit five or six World Heritage Site.You can add more easily.
1.Historic Villages of Shirakawa-gō and Gokayama(bus ride from Takayama St.)You can go and come back, before you leave for Kyoto.
2.Atomic Bomb Dome in Hiroshima
3.Sacred Sites and Pilgrimage Routes in the Kii Mountain Range which include
Kouyasan.Stay there or 1 day tour from Osaka.
not so easily,but possible
4.Iwami Ginzan Silver Mine in Shimane Prefecture.
impossible
5.Gusuku in Okinawa

P.S.
If you don't mind ,tell me why do you want to visit Akasaka in Tokyo?
I'm just curious. I think Akasaka is not typical Sightseeing spot.