Advice about train passes

I was wondering if you could please have a look at my itinerary for a trip in October and let me know if you think I am on the right track for train travel/ passes?
My partner and I will be in Japan for 19 days and plan to buy 14 day Japan Rail pass + other passes as follows:

1. Kansai airport – Osaka (purchase single ticket)
   Osaka day trip to Koyasan (koyasan world heritage ticket ltd express)
2. 2 nights Osaka (Osaka Amazing Pass)
3. 2 nights Takayama (start 14 day Japan Rail Pass)
4. 2 nights Hakone (Hakone 3 day pass)
5. 3 nights Tokyo (subway 72hr ticket)
6. 1 night Kyoto for festival
7. 2 nights Hiroshima
8. 3 nights Kyoto
9. 1 night Osaka
   10 Kansai airport(single ticket)

Any advice would be appreciated. Thanks.