These don't count for the purpose of the original post but I'm listing these all here anyway because hey, why not?
I will always, always be mad that SI☆NA's original version of FrankensenceΨ never got an official release. They deserved so much better in general, man.
There's also:
Kanazawa Tomoko's solo songs:
[2020] Romantic Tabun Comedy (RomanticたぶんComedy)
[2020] Chippoke na Jibun (ちっぽけな自分)
[2020] Kono Mama Otona ni Nacchau no ka na (このまま大人になっちゃうのかな)
LoVendoЯ's plethora of unreleased stuff, not counting Okamarin:
[2013] Jinsei Maniac (人生マニアック)
[2013] Omou ga Mama wo Shinjite (思うがままを信じて)
[2013] Ai no Gishiki (愛の儀式)
[2013] Honto no Kimochi (ホントノキモチ)
[2013] invasion ~INST~
[2013] Sweet Tweet
[2013] Oh my friend!
[2014] Crazy Lazy
[2014] DO YOU LOVE ME?
[2015] NUMBER(S)
[2015] For the future
[2015] Soushisouai (相思相愛)
[2015] Sennou (洗脳)
[2015] Gekioko! na Dekigoto (激おこ!な出来事)
[2015] Nagisa no Situation (渚のシチュエーション)
[2015] Otome no Shojijou (乙女の諸事情)
[2016] Burning Rose ~INST~
[2016] POWEЯ
[2016] girl
[2016] Answer (アンサー)
[2016] High Heel Kick (ハイヒールキック)
[2016] Ai no Uriko (愛の売り子)
[2017] in my heart
[2017] Mikansei Musume (未完成ムスメ)
There are also many songs from musicals and stage plays that have never gotten recorded releases. In particular there's the Acchii Chikyuu wo Samasun da. musical from 2004 and W's Cara & Mel musical that come to mind, as well as things like Mahou no Trump (no, not that Trump).
Speaking of W, they had those cancelled releases, but I believe they
probably pretty much all ended up on Choi Waru Devil or were repurposed as other H!P songs.
We know Fujimoto Miki was in the original recording of Onna ni Sachi Are but for obvious reasons it was re-recorded and that version was presumably deleted from existence. I'm sure there are several more examples of this happening with unexpected graduations, such as Romance no Tochuu and DOWN TOWN & Ganbarenai yo.
And the version of Gyaruru's songs that included Tsuji rather than Abe Asami. The Tsuji version of Boom Boom Meccha Maccho! was aired on the radio but I believe Onna no Ultra was never released in any form before it was re-recorded.
Heike Michiyo had a couple of songs as a post-H!P soloist that she performed that were never released. I believe Yasuda Kei has some that were performed on radio shows rather than at live events (but she also very well could have some of those). There are probably a lot more by soloists that I'm forgetting or don't know about.
One day I'll have my database fully done and tagged so I can easily look this stuff up lol.