The idea of merging them into one stream just to split them later sounds painful. I've not had a reason to do this myself, but here's where I'd start:
- When you run the docker container, create a volume such that logsit will be easy to view/ship logs from the host.
- Use something like remote_syslog2 to ship the logs to your log collector
It feels a little less-than-elegant to have to do some setup on the host as well, but if you use something like ansible where you can run a playbook and set that up during your deploy to the box it shouldn't be too bad.