I don’t remember exactly what lead up to it, but I ended up watching reruns of Voyager with my dad every day back when Spike TV was still a thing. I think that really improved my relationship with him.

More or less. I think there are some differences between the Q and K based models, but they’re close enough to not require separate ports of Rockbox.

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).