Thank you both for your replies. Erwin, I hear what you're saying about the mapping of the usernames.
J, I didn't try doing it through /home, as a) I have other things to backup that don't fall under documents, videos, audio, etc, so the symlinks wouldn't exist (and I know that making your own symlinks in LMCE is a no no, right?) and b) I agree with your second point, in that I don't think I would have write access using this method either (but I must stress for anybody else reading this, I didn't try it).
Either way, I set the root password on the core, and used the root account for the rsync ssh login, and it worked! So thank you, have been trying to do this for ages. I want to get a whole load of these into a script so I can back up my entire system with a single click.
Just need to work out how to embed the root password in the script, and I'm a happy bunny. Thanks again chaps.