What I do:
Don't mess with the authorized keys: place the key be inside the home folder as it is mounted by Ubuntu.
I know, this breaks passwordless ssh or scp into the machine because the key is not actually there. Let's find a workaround.
Run ssh username@server from a terminal, so that it will mount your encrypted folder, and now you have your key at the expected directory. (This is the default behavior in Ubuntu, when you ssh into a machine it also calls all the stuff that mounts your encrypted home, just like a local login.)
Leave this terminal open.
From this point on you can launch your scripts or scp commands. If your key had been set properly, it will work seamlessly, without prompting for a password each time.
When you are finished, log off in that terminal that you had left open in first place.
I run it all the time, with the purpose of backup too, and I find it very practical.
I am assuming:
- This encrypted home on the server actually is the place where you want your backup.
- You are not running some background process that is making magic with your backups all the time: backups commands are launched by you manually, and eventually they finish.