Changing podcast to music

How can I change a file that's showing in Podcasts, so that it shows in Music?

I've searched and I've found similar questions for iTunes for Windows, but I think there might be a different answer on the Mac.

I've tried choosing "Get Info" and then changing the details, but it still shows as a podcast.

The reason I'm trying to do this is that I want to organize and sync my content so that I have it permanently as music on multiple devices. (I don't want some of my old podcasts to only be available on my iPad when I'm connected to WiFi, for example.) I've saved the files to my computer, then renamed and re-added them, but the settings remain the same.