One idea might be to fly into a different airport in Shikoku if you're planning on leaving from Matsuyama to Hiroshima at the end of your trip. I don't know which, though.... Maybe Tokushima or Kochi?
http://www.shikoku.meti.go.jp/soshik...tion/main.html

Shikoku's big tourist attraction is the 88 temple pilgrimage - You could visit one or two ... and skip a few.
http://wikitravel.org/en/88_Temple_Pilgrimage

And the Iya Valley is one of Japan's three hidden valleys (三大秘境 Sandaihikkyo):
http://wikitravel.org/en/Iya_Valley

Maybe Alex Kerr has written about the area?... He's this forum's favourite author... [ducking for cover]

Ferry is certainly the way to get from Matsuyama to Hiroshima:
http://home.e-catv.ne.jp/tour-ehime/hiroshima2.html