I FOUND IT!
I can't believe I actually found the origin.
First I went to that Slayer page with all of info about Bemani artists and songs and saw this:
MODEL DD6
It says that the original song is 火の鳥 which means "phoenix" and it was from コナミ矩形波倶楽部 which was a collaboration of Konami musicians in the early 90s.
Searching for those two led me to this:
ƒRƒiƒ~EƒAƒ~ƒ…[ƒYƒƒ“ƒgƒTƒEƒ“ƒY'93cH Quote:
コナミ・アミューズメントサウンズ'93…秋
...
DISC 2
メタモルフィックフォース
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08. 火の鳥 (2ステージボス、6ステージ中ボス)
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The same song!
Searching for メタモルフィックフォース led to an arcade game called Metamorphic Force. It's like TMNT, except everyone is a half-human, half-animal of some sort and the music is definitely the style of Izumi.
And then right there, in the end of the 2nd stage, there was the boss, a human/phoenix hybrid with MODEL DD6 in the background.
On top of all that,
MODEL DD7 is also in this game! It plays when you face off against a female lizard/devil thing wearing almost nothing in the 4th stage. It's track 18 on that same disc called コロシアムの女悪魔 or "The female devil of the Collesium"
Also, that slayer page says that MODEL DD4 originated from "HIGHWAY" of the same group.
MODEL DD4
In the description for Model DD4 in the GF9/DM8 page, Izumi says it's from Speed King. Case closed on that mystery.
I wonder if all of the DD songs are just game music he made a long time ago.
edit: these are the games Izumi made music for, according to this page:
KONAMI KUKEIHA-CLUB
SNATCHER(MSX)
SD SNATCHER(MSX)
METAR GEAR2 SOLID SNAKE(MSX)
クライムファイターズ (Crime Fighters) (AC)
T.M.N.T.(AC)
スラムダンク (Slam Dunk) (AC)
SPEED KING(AC)
JET WAVE(AC)
Winding HEAT(AC)
FIGHTING 武術(AC)
GUITAR FREAKS(AC)
GUITAR FREAKS 2nd MIX(AC)
drummania(AC)
ヘンリーエクスプローラーズ (Henry Explorers) (Crypt Killer) (AC)
アステリクス (Asterix) (AC)
リーサルエンフォーサース (Lethal Enforers) (AC)