I've made a Docker container for running headless DSLStats.https://github.com/nallar/DSLStatsDocker#readme
It runs xvfb (X virtual framebuffer) to set up an X session without needing any real displays, starts DSLStats inside that X session, then starts X11vnc. You can connect to it using any VNC client and then set up DSL stats as required. Once you've set it up once, future starts won't require any interaction.
I haven't been able to confirm that it fully works, as my phone line is currently non-existent due to openreach problems.
Hopefully this is useful for someone else
If you've already got a machine at home running docker containers this makes more sense than running it on a raspberry pi.