Mt Fuji is in the midway of Tokyo and Matsumoto, latter of which is the "base city" for Kamikochi. So I would suggest the following itinerary.
5-Nov-16 Tokyo city tour , Stay in Tokyo
6-Nov-16 Tokyo
7-Nov-16 Activate Japan Rail Pass 7 days. Nikko day tour, come back to tokyo. Send your big luggage to Kyoto using Ta-Q-Bin.
8-Nov-16 Go to Kawaguchiko (via Otsuki) and then to Matsumoto. If you reach Matsumoto early enough (before 14:30 maybe) you can visit Matsumoto castle.
9-Nov-16 Visit Kamikochi half day and then to Takayama.
10-Nov-16 Takayama in the morning/ Shirakawa- go half day visit then to Kanazawa. Train to Kyoto
11-Nov-16 Kyoto city tour (bamboo Forest , Fushmiri inari shrine) , stay in kyoto
12-Nov-16 Nara day tour , stay in Kyoto
13-Nov-16 Return to tokyo , Take flight back
On 9th and 10th, you will do Matsumoto-Hirayu onsen-Kamikochi-Hirayu onsen-Takayama-Shirakawago-Kanazawa by bus. These are covered by 3-star route ticket, except for Hirayu onsen-Kamikochi-Hirayu onsen.
https://www.alpico.co.jp/access/ticket/pdf/mitsuboshiroute2014[1].pdf
All in all you will take
Tokyo to Nikko and vice versa.
Tokyo to Otsuki to Matsumoto
Kanazawa to Kyoto
Kyoto to Nara and vice versa.
Kyoto to Tokyo.
I think JR pass 7 days will pay off.