First thing this morning, I realised why the mirror rig-tool didn't work, and it's entirely a really dumb mistake. I'd forgotten to put the mesh pivot in the right place, and trying to fix it after skinning messed up everything.
I guess this has been a good life lesson.
So I had to re-do the skin today, and this time it's worked fine with no hiccups. So far. I've had a play around with the rig, trying to articulate the character and get some life into her.
I've also unwrapped the character, though texturing it isn't a priority for me at the moment as I'd much rather get the technical stuff looking solid before going into looks.
Also here's a silly animation I made because I got bored with rigging.