So, someone told me that if I save a new HA in the new wardrobe, my Skin will be gone, since it hasn't been unlocked in the Wardrobe, despite obviously having it on right now. I'm okay with being an Eevee forever, but I was thinking of perhaps going for a Diddy Kong look, but that's not happening, it seems?

If your Nostalgic skin is colored in https://subeta.net/wardrobe_v3.php#/skins you can use it again. If not, I suggest filing a ticket since you clearly have the skin.

Nope, it's not colored. I'll send in a ticket then. Thanks! :)