I understand that the schedule is a bit tight Yes. Your itinerary looks tight especially from the following two points.
: It is over 3 + 1/2 hours to get from Koyasan to Hiroshima.
: It is about 6 hours or more to get from Miyajima to Takayama, so it sounds hectic to stop by Himeji on the way.
I tried to rearrange sites you will reach in the first half, as is shown below, so that you will only once have to spend over 3 + 1/2 hours just to move from one to another.
will 3hrs be sufficient for Himeji I think 3 hours can be sufficient only under certain conditions.
: Himeji Castle will not be crowded.
: You are a good walker. (On the way between the entrance and the dungeon, there are steep slopes and narrow roads.)
: You will visit nothing other than the facility for visitors to see the Main Keep under restoration works.
You may hope to reach Nishinomaru of Himeji Castle or relax in a neighboring garden Kokoen.
In advance of visiting the facility you can try reservation, which is not mandatory.
http://www.himejijo-syuri.jp/en/reservation/individual.html [Example of rearrangement]
A. From KIX to Kyoto City: evening of Day 1.
B. From Kyoto City to Namba in Osaka City: evening of Day 4.
C. From Namba to Koyasan: morning of Day 5.
D. From Koyasan to Nara: morning of Day 6.
E. From Nara to Himeji: morning of Day 7.
F. From Himeji to Miyajima: evening of Day 7.
G. From Miyajima to Takayama: Day 8.
Time required for public transport
B. Kyoto -- Osaka -- Shin-Imamiya -- Namba (of Nankai)
: about 1 + 1/2 hour.
C. Namba (of Nankai, rail) -- Gokurakubashi -- Koyasan (of Nankai, cable)
= about 2 to 2 + 1/2 hours.
D. Koyasan -- Gokurakubashi -- Shin-Imamiya -- Nara.
= about 3 hours.
E. Nara -[rapid]- Osaka -[rapid]- Himeji
= about 2 + 1/2 hours.
F. Himeji -[Shinkansen #]- Hiroshima -- Miyajimaguchi (of rail) -- Miyajima (of ferry)
= about 2 to 2 + 1/2 hours.
G. Miyajima -- Miyajimaguchi -- Hiroshima -[Shinkansen #]- Himeji -[Shinkansen #]- Nagoya -[Ltd. Express]- Takayama
= about 6 + 1/2 hours.
# If you can take a Nozomi train, time for E. and G. cab be shorter.