A BIG correction by the OP!

Word 2011 does offer a "Manage Styles Used In the Document" icon in the formatting toolbar. I felt like a dummy when I finally found it. It doesn't answer my original question about whether there is a way to customize the styles offered in the drop-down style menu on a new document, but it's another way to apply the styles in use.

It does appear that the only way to modify a style is to use "Format" > "Style..." > "Modify", which doesn't require hunting around for the style in a long list if the style I want to modify is currently selected.

It's all Microsoft's fault. They keep changing things . . .