Hi Craig,
do all your grounds go to one common spot (like the back of the volume)? If there is more than one path to earth you can get a ground loop in the guitar.
Do you have the wire to the bridge connected?
Are all the joints good?
No shorts at the jack socket?
Last but not least, you are not doing this near a computer, TV or flourescent lights? All those induce hum in single coils anyway.
Good luck, I know it can drive you crazy.
Phil