I've set up my numbered styles just as I want them, using resources and links
I found here. I think they are set up properly (famous last words!). They've
been working great, but in all my documents so far, the numbered section has
been at the end of the document.

Now I have a document with a numbered section, followed by another
paragraph, then another numbered section, which I want to restart. Whenever I
apply the numbering style to the second section, it continues numbering from
the first.

Any suggestions?