Sounds like an interesting idea!
I can only think that the large size of the coil is contributing to the hum.... the bigger the coil, the more hum you get.
Do you have all the metal parts grounded? The braided shield should be soldered to the base plate, and the pole pieces should be grounded as well.
Just as a test, try wrapping the whole thing in aluminum foil, grounded to the base plate, and see if that helps... this would at least give you an idea if it's the coil picking up hum.
I have a bunch of those strat pickups which I have been harvesting the ceramic magnets from for trying out pickup ideas. They are pretty good magnets.