Here is an example of an okunoshima tour itinerary for your reference. I wanted to respond back to a comment from a visitor to this blog but could not due to system complications. I am out of reach to my PC for the time being. Let me try submitting an article for her reference.
Okunoshima access (ferry &train table)
http://www.qkamura.or.jp/ohkuno/access/images/jikokuhyo.pdf
There should be a JR train arriving at TADANOUMI Stn from MIHARA at 9:52 (this could be updated in the middle of March by JR).
Leave TADANOUMI Port by ship at 10:05;
Arrive on the island at 10:17;
Leave the island at 12:45;
Arrive at the port at 12:57;
Leave TADANOUMI Stn for MIHARA at 13:15;
Transfer at MIHARA and go to HIROSHIMA.