How do you upload a snapshot?
Basically, as you said. Mount the data somewhere and back up its contents.
I back up snapshots rather than current data, because I don’t want to stop the running containers that read and write from that data. I’d rather avoid the situation where the container is writing data while it’s being backed up. The back up happens shortly after the daily snapshot is made so the difference between current and snapshot data is small.
Logcheck. It took ages to make sure innocent logs are ignored, but now I get an email as soon as anything non-routine happens on my servers. I get emails with logs from every update, every time I log in, etc. This has given me the most confidence that nothing unexpected is happening on my servers. Of course, one needs to make sure that the firewall is configured well, and that you use ssh keys etc., but logcheck is how I know I’m doing enough.