As well as the `--default-owner-` switches, I had some file permission issues on the Docker side. I ended up using `setfacl` to enforce really permissive permissions on `~/mysite` on the VM side, otherwise some Docker containers would complain. It turns out Docker for Mac fakes some file permissions, which is why it wasn't a problem before.
Other than that, it mostly just worked! Feel free to get in touch if you have more specific questions.