I did a brief tally just by typing in the destinations on
Hyperdia | 乗換案内 路線検索 時刻表 ゴルフ場 旅費精算 通勤費なら and including the Tokyo-Kyoto initial trip, you surpass the 21day pass price on your Toyama to Matsumoto leg (60,000yen+).... Granted, some of the trains aren't JR and you would have to pay for them, but not too many. I also haven't included the Matsumoto to Tokyo, the round trip to Nikko (Hakone would use a private railway), which could fetch another 19,260 yen.... For a total of about 80,000+ yen/person....
I took a 7 day pass and I went to Shizuoka, Nagahama, Nikko, and Kyoto from Tokyo as well as using it on the JR lines in Tokyo and for the 28,300yen price, I spent the equivalent of 65,000yen....
If I were you, I'd buy the 21 day pass....
You can purchase it at Narita airport and activate it right away for use on the trip into the city! Be advised that it's good practice to reserve the seats in advance so as to ensure availability. And for the trip to Kyoto from Tokyo, ask for seats on the right side of the train so you can get an unobstructed view of Fujisan (Mt. Fuji). You could ask the JR employees at each station you leave which side of the train has more scenic views. Some of them may be able to tell you.