ZFS. Snapshot the entire filesystem, ship it off somewhere. Done. At worst, Postgres is slow to startup from the snapshot because it thinks it’s recovering from a crash.
As a side note, it's pretty interesting TrueNas is heavily designed around the ZFS paradigm. Most people think of applications and time stamps to restore not data pools and the snapshot paradigm accompanying ZFS.
With the right layer of abstraction on top of snapshots one could have the cake you need it to as it is difficult for beginners to grasp ZFS.
https://utcc.utoronto.ca/~cks/space/blog/linux/UbuntuKernels...
Well, the people who host the people do. Is that not argument enough in favor of it?