Thank you all! I was able to create a Docker container running the BOINC server and connect it to a remote MySQL instance. In the end, it came down to figuring out the right dependencies and configuring make_project for a new project or config.xml for an existing one.
While testing the addition and removal of dependencies to reduce the image size, I noticed that one library—libapache2-mod-php—significantly increases the final image from ~400MB to ~1.5GB. I plan to explore replacing it with smaller libraries in the future and just wanted to share that observation.
Thanks again, everyone, for the feedback!