Do you think it would be cost wise to purchase the 21-day pass? That is mere waste of time and money, I think.
For your planned trips,
a 21-day Japan Rail Pass is definitely too expensive.
You have a non-JR train or bus ride (which is not covered by JRP)
at least for the following sections.
: Matsumoto -- Hirayu Onsen -- Kamikochi (by bus).
: Kamikochi -- Hirayu Onsen -- Takayama (by bus).
: Otsuki -- Shimoyoshida or nearby station
(by Fuji Kyuko).
: Ito -- Izukyu-Shimoda or nearby station
(by Izukyu [Izu Kyuko]).
Kyoto (3 days), Fujiyoshida (3 days), Minamiizu (3 days) and Tokyo (2 days) Fujiyoshida City is at the north foot of Mount Fuji.
Minamiizu Town faces the Pacific Ocean.
These two destinations of yours are far apart from each other.
It sounds better, both time wise and cost wise,
to visit Fujiyoshida and Matsumoto in this order
and go directly from Kyoto to Minamiizu (#).
In this case,
making a combination of
a JR East Pass (Nagano, Niigata area),
JR regular tickets
and Fuji Kyuko regular tickets,
you can put down your railway cost for major legs
to around 42000 yen (+/- about 1000 yen).
The Izu Kyuko Line is covered by this JR East pass.
This JR East Pass
is valid for the selected 5 days within the 14 days from the day of issuance.
You plan to stay for 13 nights outside Kanto Region.
So,
to make this JR East Pass cover your interregional train rides around Kanto,
you have to wait for your timing of purchasing this pass
until the day when you first travel to another region.
This JR East Pass can be used
for Tokyo -- Shinjuku -- Otsuki,
for Otsuki -- Kofu -- Matsumoto,
for Atami -- Ito -- Izukyu-Shimoda,
and for Izukyu-Shimoda -- Ito -- Atami (by non-Shinkansen lines),
on 4 different days during the 14-day period.
- Japan Guide: JR East Nagano Niigata Area Pass
https://www.japan-guide.com/e/e2361_nagano_niigata.html- East Japan Railway Company [JR-East]: JR EAST PASS (Nagano, Niigata area)
https://www.jreast.co.jp/e/eastpass_n/- JR-EAST Train Reservation
https://www.eki-net.com/pc/jreast-shinkansen-reservation/English/wb/co...: This seat reservation system may work for your train rides mainly on Day 2 and later days.
: You have to pick up the tickets
by 21:00 (Japan Standard Time) of the day before the boarding date.
: Your credit card of a designated brand is required.
The following JR regular tickets for your trips
can be purchased together at once at a JR ticket window.
: One-way basic-fare ticket for Takayama -- Nagoya -- Kyoto.
: Reserved-seat Limited Express ticket for Takayama -- Nagoya.
: Reserved-seat Shinkansen ticket for Nagoya -- Kyoto.
: One-way basic-fare ticket for Kyoto -- Atami.
: Reserved-seat Shinkansen ticket for Kyoto -- Atami.
(#) To travel by railway in your (now-planned) order of the places
from Kyoto City via Fujiyoshida City and Minamiizu Town to Tokyo,
you take a very roundabout route.
: From Kyoto
via Atami, Shin-Yokohama or Yokohama and Hachioji to Otsuki,
round trip to Shimoyoshida (or nearby station),
from Otsuki back to Atami,
round trip via Ito to Izukyu-Shimoda (or nearby station),
from Atami back for Shin-Yokohama or Yokohama,
then to Tokyo.