Of course you are more than welcome!
Here is an example of your Journey to Miyajima,
Kyoto --> Miyajima ¥ 11,110 + ¥ 170 for Ferry / Free with JR Pass
A return would be ¥ 22560.
One way takes a little more than 3 hours, so you would spend more than 6 hours in the train that day, if that is too much consider staying the night in Hiroshima.
The journey itself is quite straightforward so I don't expect any problems.
What to do in the last 3 days?
All the destinations you listed are great! Let me put it this way:
What would you like to see/visit the most?
Hakone: Beautiful nature, lakes, forests and a breathtaking view of Fuji.
Kanazawa: A very charming town, with history, beautiful geisha quarter, caste and great mountain views over the city.
Izu Peninsula: Beautiful coast lines and great hot springs (onsen).
Mount Koya: Great Hiking tracks and an enchanting nights-stay at a Temple
Personally I would either go to Hakone or Kanazawa, if you have had enough travel from your return to Miyajima, Kanazawa is probably the most practical, because there is a direct express train between Kyoto and Kanazawa. So you get in and ride to your destination without further hassle.
In your situation I think a 7 day rail pass is best, with your return to Miyajima you will already have covered most of the costs (¥ 22560 of the ¥ 28300 cost) and with anymore travel to any of the destinations except for Mount Koya you would be sure to make some good savings. For mount Koya you have to ride a non JR-line from Osaka so only in this case a JR-Pass would not be the best option. I would the 7 day JRPass in the last 7 days of your trip, this way you can use it for your trip to Nara and the return to the Airport as well!
Hope this helps and let me know your thoughts!