I am a complete idiot - I thought I had got CP up to date, but I hadn't. I can't believe I missed something so obvious
I deleted the data directory and cloned CP from GitHub. Now it works perfectly with NZB 360 v8.4.3.
For reference, my CP version is now 75a8529 (17/7/2014 21:24:48) git, master
Sorry for all the hassle guys.