Hi there!
First let me say that I really like this plan, the area around Matsumoto - Takayama -Kanazawa is very beautiful and one of my favorites in Japan.
As for the JRPass, I'd guess that you are wondering what would make more sense: the 14 day or 21 day JR Pass. I see that you are moving around a lot from day 7 to 20, now if you would plan your day trip to Nikko on day 6 than you could cover all for your long distance and pricy travel in the 14 day JR Pass validity period. So a 14 day JR Pass would be a good pick in any event.
That is not to say though that a 21 day JR Pass would not pay off either. The difference in price with the 14 day JR Pass is 12,600 and this is easily traveled in a week. For instance your travel from the Airport to Tokyo would be covered, this is 3000Yen if you take the Narita Express to Tokyo. Will you be flying back on day 20? Otherwise you could also use the JR Pass to travel to the Airport the next day. There are a couple more perks like this that are very nice, for instance you can take the Bullet train to the front door of Hakone and travel and JR Line in and around Tokyo without having to buy any additional tickets. Basically with the 21 day JR Pass you buy a little more flexibility.
Either way a JR Pass would work out great! I don't know your plans for Hakone but a you may find a Hakone Free Pass useful there. So I'd certainly recommend looking into it.
Enjoy Japan!
-Daniel
