Owain,
Attached is a photo of my half-round miniature file laying in the timing-side thread. (The file is from a common set.) To me, it looks like a pretty good fit (the tip of the file is not in the focal range). I'm not swearing that this is the best (or even a good way to do it), but, if it was mine, I'd try it on a bit of the thread to see what I got. I've had some success with this particular file on even finer threads.
Otherwise, if you want to buy the die, I'd chip in 25% of the 18 GBP price if it became a forum-wide loaner.
Richard L.