The only pic where you can see her full costume, it might be nothing, or might be something, but that brooch she’s wearing seems to have a huge green stone or something in it.
When I look at that picture the first thing that comes to mind is “Mrs. Gulch”, The Wicked Witch’s alter ego. So I googled Mrs. Gulch and while you have to account for the time period – the style of dress could be similar. So if she is going to be the Wicked Witch it would make sense for her SB character to be Mrs. Gulch. And Mrs. Gulch has her own theme song.
Image of Mrs Gulch
I think you’re on to something. The skirt Mader is wearing is really just updated, less prim, version of the one worn on the Wizard of Oz.
As to the theme song: everyone knows the Wicked Witch of the West/Mrs Gulch theme song, you’re right.