Figured it out. :)
First, you need to bring up the Manage Styles dialog...
You can get to this via the Styles panel, which itself is accessed via the little dialog launcher at the bottom-right of the Styles ribbon section. Once the Styles panel is visible, click the Manage Styles button at the bottom of it (it looks like a little pencil editing the usual "AA" icon):
Next, you need to edit the Hide-Until-Used property of each of the styles you want to show. On the Recommend tab, find the built-in styles you're after, highlight them, and click the Show button:
For me, that was enough to show the styles I wanted in the Quick Styles Gallery.
However, if you're trying to show a built-in style that doesn't normally appear in the gallery, you'll need to go to the Edit tab, select the style, and click Modify. The Modify Style dialog will appear and, in that, you need to select the Add To Quick Style List option.
Job done. :)
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. :)
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