Your post raises a number of questions, actually.
So you are flying down to Kagoshima for over 6 weeks?
Why?I've traveled the same routes you did, around the same time. Never had any problems getting a seat at all.
So you may be blowing your whole thing out of proportion. You also might look at getting the JR Setouchi Area Pass instead - it's a bit cheaper though seating is all unreserved. And if you are trying the chase the cherry blossoms, you also might consider a few other places. Iwakuni was absolutely delightful in cherry blossom season, and the mountaintop castle gave an excellent view over the whole area.
https://youtu.be/0COOZXi66mMAlso your idea of seeing Hiroshima and Miyajima in half a day or so is just not realistic. Both together will easily fill up a whole day. Miyajima also has a number of great places for cherry blossoms, and is not a place you want to rush through.
https://goo.gl/fAz4axIf you get lucky, you can see Miyajima both at high tide (when the shrine looks better) and low tide, where you can walk on the beach up to the giant torii gate.
You could also spend a full day in Takamatsu - it is one of the more interesting cities on Shikoku. The Ritsurin Garden is a must-see place.
https://youtu.be/afx-Ju52FiYAnd Yashima + Shikoku Mura are worthwhile too.
https://youtu.be/EQgQ9V3qk38I would stick with the IC cards in Kansai, unless you travel long distance like a day trip to Himeji. In Tokyo, the 2-3 day subway pass can save some money.
http://www.tokyometro.jp/en/ticket/value/travel/index.html#anc03In Fukuoka the Tourist Pass is good if you think you'll also be taking the bus. But many good sights are close to a subway station, so a subway day pass might suffice very well. As for what to see, try looking through:
http://www.thejapanfaq.com/fukpic.htmlOne place you should not miss is the Nanzoin Temple just outside the city. There is also one of the nicest cherry blossom spots along the way, Kayoichi Park, in Kasuya. And almost unknown to everyone.
https://youtu.be/pYKNmvevAC4Inside Fukuoka, two excellent blossom places are Maizuru Koen and Nishi Koen, both near Ohori Koen, so very convenient.
http://bit.ly/1KAm8cUThe airport in Fukuoka is very conveniently located, but in other cities are far less so - rail would be the ideal way to travel.