There are only about 5 groups, and each group has about 20 terms--yes they are static.
I think I found a way to do this--I added the "content: taxonomy terms on node" and "taxonomy term: parent term" relationships to the view.
The key is the "taxonomy term: name" criterion has a checkbox where I selected "parent", which appears only after you add the relationship. I added the post-date sort criteria after that, and it appears to be working the way I want.