CAUTION: This post is mostly a note-to-self, for Future Ben.
According to the GitHub blog post, you can add a _config.yml file to tell Jekyll to "include" the "node_modules" and "vendors" directories. I don't know anything about Jekyll (or even that this is what was powering GitHub Pages); so I tried creating a _config.yml file. To no avail. Nothing changed.
Apparently, according to the GitHub support ticket I opened, _config.yml only works if you're actually using Jekyll in your GitHub Pages branch:
Sorry for the confusion here.
We recently moved to Jekyll 3.3. which ignores the "vendors" folder by default.
A _config.yml file will only work if you are using Jekyll, so the .nojekyll is your best bet.
Since I'm not using Jekyll - since I thought GitHub pages was just "HTML" - I created an empty .nojekyll text file in the root of my gh-pages branch. And kablamo! It started working again!
Future Ben, you're welcome.