I wired this, I thought it was correct but Im still waiting on strings to put it together. I can switch the 3way and the pickups change but there is a constant buzz and not sure the volume is affecting the signal....
The first thing that springs to mind is a Tele schematic without the tone pot.
I can't see why it wouldn't work.
For the second matter try shielding all the cavities with copper foil or conductive paint...see http://www.guitarnuts.com all about shielding.
Use the conductive paint. The foil can be a real pain...but it works.
Good luck
Robbo