OK, I tried creating a ssh key as root and copying that to my home server, that seems to work - at least it does for running the upload-backup with sudo.
For reference, here's what I did:
Created a "symbiosis" user on my linux box
Allowed SSH on port 22 through my router firewall to the linux box
Configured the router with a dynamic DNS service
On the symbiosis server, put "firstname.lastname@example.org:/home/symbiosis/backup" in /etc/symbiosis/dns.d/backup.name
sudo su -
Synchronise the backups with