I think I've solved the buzz. Most of it went away when I put a strip of tape across the underside of the pickguard, and made sure it touched on both sides. But I ran out of tape to fully cover it, and even so had to put a bit of aluminium foil in to fill in a gap. But as soon as that seal was made the buzz dropped drastically.
I'm not sure if covering it more will reduce the buzz even more. I'm not sure if all guitars just have a little bit of buzz or if it's actually possible to get it near zero.
My local shop has a TUSQ nut in stock for $14, so if PBG don't get back to me with one I think I will just go and get that. I will have solved all the problems except for the trem not returning to the exact same spot. But it sounds like Colin couldn't get that to work from his build either.
At 33 after playing guitar since I was 5 I feel like it is waaay too late to play right handed :P I feel like a complete beginner with a cramped left hand every time I try.