Note that my first F-Droid attempt, the "lagrange-fdroid" repository on GitHub, is gone. It was not working properly because the raw HTTPS URLs did not serve HTML pages with the right MIME type, and anyway the repository had incorrect mirrors in the configuration. If you have it installed on F-Droid, delete the repository in Settings and install this new one on skyjake.github.io.
I removed the wildcard MIME type from the app manifest that made the app want to open all kinds of files. Now it only opens Gemini/Gopher/Finger URIs. I attempted to make it allow .gmi files as well, but on my phone it didn't seem to be working. YMMV.
Due to my lack of Android experience, I'm not 100% sure what the convention is regarding downloaded files, but at least now they are visible somewhere.
The Android-specific repository with the Java sources (mostly from SDL) is now available, too:
🏷 Android, Lagrange