It's time to admit that I made a rather embarrassing mistake. I was just about to order my revised PCBs from OSH Park, when I spotted some text that made the blood rush to my face:

Detected 2 layer board of 1.54x0.71 inches (39x18mm). $5.45 for three.

It wasn't a hot flush from the excitement of spotting a deal, it was a blush from the realisation that my board doesn't actually fit in one square inch when on the diagonal...

As a result I'm sadly going to have to withdraw from the square inch project. Whilst the prizes looked great, none of them can compete with the prize I stand to win when I complete this project: my girlfriend's heart (or at least an end to the annoyed looks she gives me when I ignore her because I'm working on the valentines present I promised her 3 years ago!).

Anyway... Lesson learned: Actually measure stuff rather than just assuming it fits because it's small!!!