How to change logging driver on a running container in docker

I've got a running container with the default logging driver json-file, and would like to change it to syslog (new default). The docker engine's configuration has been updated to use syslog by default, so creating new containers w/o specifying the logging driver uses syslog. Is it possible to change the logging driver on existing containers without having to recreate them?

docker update command doesn't support it, editing container's config.v2.json and restarting the container seems to have no effect.

Based on this and this documentation it seems impossible to change the log driver of a docker container. One could change it to rerun the container.