Restart container on a schedule with Start before stopping

I have a container which does an import process on startup. The imported data is updated on a daily basis, and I would like to schedule a corresponding restart of the container so the process is serving the most recent data. Further, I’d like to do this with no down time, such that the new container instance is started and healthy before the old instance is stopped. I believe this is the equivalent of doing an Upgrade with Start Before Stopping enabled, but there is not necessarily an upgrade of the container image involved.

We are currently using container-crontab for another scheduled task - is it possible to use the same here?