Thanks all, I'll play around with the nut first, and it looks like I have more saddle adjustment room than I thought. Pushing the string down at the 3rd fret there is definitely more than 1mm just eyeballing it, so I'll start there.

A couple of other problems: I keep breaking the wires at the solder points, I'm going to run out of wire at this rate, so I'll have to find some more to extend it, some of that shrink wrap I bought years ago might help here too. I also plugged it in to see how it sounds and ironically the humbucker makes the most buzz. The volume pot is also buzzy when it isn't on full.