Hi Matt,
It feels a bit busy to include all these places, especially going down to Nagasaki adds a lot of travel time.
I think you could do Okayama, Kurashiki and even Onomichi in a single day if you plan it well. Or combine one of those places with a visit Himeji. Then do one or two days in Hiroshima, especially if you want to include Miyajima as well.
From Hiroshima it is already 5 hours to Takayama, it will be around 8 if you come from Nagasaki. If you do want to include Nagasaki, then I would suggest starting there and making your way up to Hiroshima and the other cities.
Hope this helps!
Daniel