When will you travel? In what month?
Later in 2023,
the prices of the Japan Rail Passes will be increased drastically.
https://www.japan-guide.com/news/japan-rail-pass-cost-increase.htmlOn the condition that you fly out of Japan from Fukuoka Airport [FUK],
14-day JRP is not suitable for your itinerary.
Note: JRP travelers cannot choose Shinkansen NOZOMI or MIZUHO.
I also noticed you cant use it through electronic gates on stations and have to show a "guard" your pass. Your source seems too old.
Japan Rail Pass got redesigned to be a magnetic paper ticket,
three years ago in June, 2020;
so, you can get through automatic ticket gates with your JRP.
How long will you be in your listed places?
Have you decided where in Tokyo | Kyoto | Osaka will you stay?
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Estimated costs per adult, with your Shinkansen seats reserved.
Narita Airport -- Tokyo (somewhere)
: About 1300 to 3100 yen.
Tokyo (somewhere) -- Shinjuku -- Odawara
: About 2100 to 2400 yen,
JR or subway + Odakyu ["Romancecar"].
Odawara -- Hakone-Yumoto -- Odawara
and various routes in Hakone
: Up to 5400 yen, with 3-day Hakone Freepass;
not covered by any JR-issued pass.
Case (A)
: You travel from Odawara to Hakata
in more than 7 calendar days.
(A) Odawara -- Shin-Ōsaka -- Hiroshima -- Hakata
: 30700 to 32500 yen.
(Plus 530 yen each for "NOZOMI or "MIZUHO".)
(A-1) Odawara -- Kyōto
: 12100 to 12700 yen,
JR Tōkaidō Shinkansen ["HIKARI"].
(A-2) Kyōto -- Shin-Ōsaka
: 580 yen,
JR Kyōto Line [Special Rapid].
(A-3) Shin-Ōsaka -- Hiroshima then Hiroshima -- Hakata
: 18020 to 19220 yen,
JR San'yō Shinkansen ["HIKARI" or "SAKURA"].
(Plus 530 yen each for "NOZOMI or "MIZUHO".)
Case (B)
: You travel from Odawara to Hakata
within 7 calendar days.
(B) Odawara -- Shin-Ōsaka -- Hiroshima -- Hakata
: 26600 to 28400 yen.
(Plus 530 yen each for "NOZOMI or "MIZUHO".)