Hi Wayne,
Let's have a look at ticket prices and find out:
Kansai Airport - Osaka ¥ 1,160
16/5 – Osaka > Nara > Osaka ¥ 1,560 (for the return)
17/5 – Osaka > Kyoto ¥ 540
20/5 – Kyoto > Miyajima > Kyoto ¥ 22,220 for the train and ¥ 340 for ferry.
21/5 – Kyoto > Kanazawa ¥ 6,710
23/5 – Kanazawa > Takayama ¥ 4,180
25/5 – Takayama > Hakone ¥ 12,410 (to Odawara station)
27/5 – Hakone > Tokyo ¥ 3,640
31/5 – Tokyo > Osaka ¥ 13,750
Osaka - Kansai Airport ¥ 1,160
For a total of ¥ 67,670 the 21 day JR pass is ¥ 57,700 so you would make ¥ 9,970 in savings. In addition the JR Pass is valid for local travel on the JR Network in both Tokyo and Osaka, so you would probably end up making even more savings.
An alternative option would be to use a 14 day JR Pass from the 19th - 1st, this way you would make the followings savings.
20/5 – Kyoto > Miyajima > Kyoto ¥ 22,220 for the train and ¥ 340 for ferry.
21/5 – Kyoto > Kanazawa ¥ 6,710
23/5 – Kanazawa > Takayama ¥ 4,180
25/5 – Takayama > Hakone ¥ 12,410 (to Odawara station)
27/5 – Hakone > Tokyo ¥ 3,640
31/5 – Tokyo > Osaka ¥ 13,750
Osaka - Kansai Airport ¥ 1,160
For a total of ¥ 64,410 or ¥ 19,310 in savings as the 14 day JR Pass is 45,100yen and buy normal tickets for the rest of your itinerary.
Hope this helps!
Daniel