Syncthing is excellent for phone sync.
What I did was have it running on a system in the network of the nas, mount the nas on that system, and place the backups folder in the nas.
If you have a system that reliably runs, or can get syncthing running on the nas, I recommend doing that.
Synology has docker iirc, there aught to be a syncthing container.
Else, slapping a pi zero into the nas' network should do the trick and be fully independent of what the nas is.
What is the threat szenario?
If you are smart about parallelization and have access to custom hardware, couldn't you turn 5 days into 1 hour or less?