I clicked "Start fresh" on the Audio page but the track list still shows the wrong sections. Did it work?

Yes. "Start fresh" removes the cached narration and all rendered files right away; before version 1.9.12 the track list itself was only rebuilt by the next render, so it kept showing the old rows until you clicked "Render". Since 1.9.12 the list is rebuilt immediately from the book's current sections, so what you see after "Start fresh" is exactly what the next render will produce. Your voice, speed and narrator name are kept in both cases.