Thanks to everyone that posted suggestions.

I liked Shonky's connector idea but couldn't see a way to get it to work with my design that has components alone every edge. I'm probably going to go with genixia's chopping board suggestion and use the Farnell probes I posted at the top of this thread. I have a Dremel, so it should be fun making a little jig. Plus, a chopping board will give me enough material to make a few attempts if the drill wanders and I don't get the holes for the probes just right first time.

I did think about using an old smart-card connector (the sort you find under the battery in mobile 'phones), so that might be my backup plan.

I'll let you know how I get on. Thanks again.