OK, I just played around a little more.
Our original aim was to have subheadings for years, but sortby=”author” within years. I assumed this was possible because of the help text under Display > title (“Note: The “order” and “sortby” attributes will act as a secondary sort”).
I now realized that if you combine sortby=”author” and title=”year”, the headings instead get sorted by author. The way to go for us seems to be [zotpress title=”year” sortby=”date” order=”desc”], even if we lose alphabetical order within the yearly sections.