Found an NES version of Doki Doki Panic on eBay! Thought it'd be a hack of the original sprites on top of Mario 2 but this appears to be the original game!
Doki Doki Panic English translation (Papa gameplay and True Ending) - Vizzed.com GamePlay (rom hack) - YouTube
Yume Koujou Doki Doki Panic (Japan) [En by Vice v1.0] (~Dream World Doki Doki Panic!) ROM < FDS ROMs | Emuparadise
Yume Koujou Doki Doki Panic [b] (J) ROM Download for Famicom | Gamulator
Corona Jumper: Super Mario Bros 2 (NES, 1988)
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NES – Doki Doki Panic | Obscure Video Games
Yume Koujou : Doki Doki Panic ROM NES
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Doki Doki Panik! By MB Hacks (SMB2 Hack) ROM - NES Download - Emulator Games
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Nintendo NES Video Games Panic! for sale | eBay
DREAM WORLD DOKI DOKI PANIC! - Nintendo Famicom Disk System (FDS) rom download | WoWroms.com