Turns out this is a very difficult thing to do. Super Lightswitch-hacker David Baker saw a post I'd made on the subject in the MSDN Lightswitch forum, and kindly offered to have a go at it for me. It took him several goes, but we got there in the end.
I wouldn't recommend this to anyone. I would strongly recommend using an external database right from the start. I can't see much benefit from using the internal one, and if you ever need more control over it, or want to switch to an external one, you've got major problems.
Hope this helps someone.