I ended up having to dig into the editor's source for this:
First, in VisualLineTextParagraphProperties.cs, I had to expose the TextAlignment via a new internal property (defaulted to LeftAligned), so I could set it (and, of course, return it from the getter of the public property).
Then, in TextView.cs, in the BuildVisualLine method, I had to test the text of documentLine for the conditions under which I wanted the line centered, then change the paragraphProperties object accordingly.
Do note that I had to make a copy of paragraphProperties - otherwise the centered alignment would bleed over into the next line (because the given paragraphProperties object seems to be reused).
Also note that I could not find a way to use a VisualLineElementGenerator to do this - even though it still looks to me like that would be the place to change something like TextAlignment...