Word 2007: style name already exists or is a built-in style... but I can't find it!

While I'm not sure how things got in the state they did, I've now found the "Section Heading" style and removed it, allowing me to add my own style with that name. Here's what I had to do:

From the Styles section of the ribbon, click the bottom-most of the 3 buttons at the right of the Quick Styles Gallery. From the menu that appears, select the Apply Styles option. The Apply Styles panel will appear; in that, type the name of the style you want to create (in my case, "Section Heading"):

Once you've typed the full name of the style, the New button changes to Apply (because the style already exists) and the Modify button becomes enabled. Next, just click the Modify button. Here's what appeared for me:

So, it looks like "Section Heading" was some kind of alias for the "Title" style. And that's why it wasn't appearing in the Manage Styles dialog - it was only listed as "Title".

As I said, I've no idea how it got in that state (I'm pretty sure the original author didn't intentionally use paragraph styles), but I hope this helps anyone else who might come across the same weirdness. :)