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You should look into Rockbox. It’s an open source alternative firmware for a variety of portable media players that adds features such as support for more file formats (and it runs Doom). As for which supported players I’d recommend then maybe a flash modded iPod or an AIGO Eros Q or K (also sold as the HIFI WALKER H2, Surfans F20, or AGPTek H3).
Have you tried Mystery Dungeon? I think there are four of them on Switch. There’s Shiren the Wanderer 5 & 6, Chocobo’s Mystery Dungeon Every Buddy, and Pokémon Mystery Dungeon: Rescue Team DX. If you’ve never tried the Mystery Dungeon format, then I’d recommend playing the demo for the Pokemon one to see if you like it first.