I don’t have a Dockerfile because it’s a Python application so I just followed the quickstart. I changed the mount point to be /workspace/data, which is what the folder you were referring to is.
Then it started giving me permission errors, which I found here Can't create Sqlite database in mounted volume - #2 by sudhir.j
As stated in the thread, I first ran ls -la workspace/data to see who owned what, and I noticed that a subdirectory was owned by root instead of cnb. Running chown -R cnb:cnb workspace/data fixed that issue.
Then I had some issues with relative paths and zipfiles, but that was a straightforward fix in Python (by specifying arcname to ZipFile.write).
Thanks a lot for the help!