Should I get a 14-day or 21-day Japan Rail Pass for this intinerary?

Would really appreciate if someone can explain to me if it is worth getting a Japan Rail Pass and for how many days for the below itinerary. I posted the question on TripAdvisor and one person commented I should get the 14-day pass for April 2-15.

I used google to calculate the cost of individual trips and then use Hyperdia to see if the Japan Rail Pass covers these five most expensive trips that total more than 59,350 YEN (cost of 21-day pass):
1) Tokyo to Osaka (Nagahoribashi or Namba Station)
2) Osaka to Miyajima to Osaka
3) Kyoto (Kawaramachi Station) to Kanazawa
4) Kanazawa to Yudanaka
5) Yudanaka to Kawaguchiko

I accounted for the trains that are not covered by Japan Rail Pass (which I came across on this forum). If my research and calculations are correct, it is worth getting the 21-day pass. Does a 21-day pass sound right or am I missing something?

Thanks.

3/30/2017 Tokyo - Arrive in Tokyo ~4pm (hotel by Shinjuku station)

3/31/2017 Tokyo - Ueno Park, Chidorigafuchi, Inokashira Park

4/1/2017 Tokyo - Kumagaya Sakura Tsutsumi, Meguro River

4/2/2017 Tokyo-Osaka - Tokyo to Osaka, Osaka Castle Park (hotel by Nagahoribashi and Namba stations)

4/3/2017 Osaka - Cherry blossoms and deer at Nara Park

4/4/2017 Osaka (Kyoto) - Maruyama Park, Philosopher’s Path, Kiyomizu-dera

4/5/2017 Osaka - Himeji Sakura Festival

4/6/2017 Osaka - Miyajima

4/7/2017 Osaka - Cherry blossoms at Mount Yoshinoyama

4/8/2017 Osaka - Dontonori, Shinsaibashi

4/9/2017 Osaka-Kyoto - Osaka to Kyoto, Gion (hotel by Kawaramachi station)

4/10/2017 Kyoto - Fushimi Inari-taisha Shrine, Kinkaku-ji

4/11/2017 Kyoto - Arashiyama (Bamboo forest)

4/12/2017 Kyoto-Kanazawa - Kyoto to Kanazawa, market (hotel by Kanazawa station)

4/13/2017 Kanazawa - Kenrokuen, districts, castle

4/14/2017 Kanazawa-Nagano (Yamanouchi) - Kanazawa to Nagano (Yudanaka)

4/15/2017 Nagano (Yamanouchi) - Jigokudani Yaenkoen (hotel pick up at Yudanaka Station)

4/16/2017 Nagano-Tokyo-Fujikawaguchiko - Nagano to Tokyo to Kawagushi (hotel pick up at Kawaguchiko Station)

4/17/2017 Fujikawaguchiko - Arakura Sengen Shrine/Chureito Pagoda, Lake Kawaguchiko

4/18/2017 Fujikawaguchiko - Fuji Shibazakura Festival

4/19/2017 Fujikawaguchiko-Tokyo - Lake Motomuso, Fujikawaguchiko to Tokyo (hotel by Shibuya station)

4/20/2017 Tokyo - Tsukiji fish market, Takeshita Street, Shibuya Crossing, Nakamise-dori, Akihabara

4/21/2017 Tokyo - Depart Tokyo