I am mainly looking at travel time. Several people have suggested an extra day here or there, my suggestion would be to take an extra day in Takayama. You might take one of the day trips offered by the Nohi bus line, which is out of Takayama. I would drop a day in Tokyo.
How about this:
Traveling around Kyoto usually is done by bus. You will not need a train pass.
From Kyoto, travel by bus (Nohi private line) to Takayama. It takes about an hour longer by bus than by train, but you will not have to switch trains in Nagoya. Most people traveling by train will take a Shinkansen to Nagoya, and then a wide view limited express train to Takayama. It is also possible to take a direct limited express train from Kyoto to Takayama. This train links up with the limited express departing from Nagoya at Gifu Station, and the two trains continue together to Takayama. The direct train itakes about 20 minutes longer than the Shinkansen/L.E. option.
My suggestion is to take the Nohi bus line:
https://www.nouhibus.co.jp/english/If you go to the link, you can find out about some of their tour pakages, as well as the timetables for the Kyoto to Takayama .
From here, I would again travel by bus from Takayama to Kanazawa. This goes through Shirakawa-go, and you may want to stop here and look around. This can also be done by train, but since Shirakawa-go has no train station, you will not be able to go there.
From Kanazawa, Activate a 7 Day JR Pass, and go to Tokyo. There is now a Shinkansen from Kanazawa to Tokyo, so it is a lot faster. Visit Tokyo.
From Tokyo, I would go to Okayama, and stay there. I would actually do this in the late afternoon or evening. Hiroshima is only one hour away by Shinkansen, and Naoshima is also nearby. I would do Hiroshima, Miyajima, and Naoshima from here. Okayama also has a very nice garden to visit. If Okayama is not interesting enough for you, think about staying at Kurashiki for several nights:
http://www.japan-guide.com/e/e5750.htmlIn Tokyo, you would spend only four nights there, and on the fifth day, visit Tokyo before you spend 2 nights in Okayama or Kurashiki. You would do your two day trips from here, and then travel that evening to Osaka before the pass expired.
If you spend a day less in Tokyo, you would have an extra day (and night) at Okayama or Kurashiki before heading back to Osaka.
This plan adds a bus ride to Takayama, and cuts the JR pass from a 14 day to a 7 day.
It is worth considering.