The bad earth on many basses is often from the wire either being pushed into the wood or what looks like sinking into the finish as if it was bolted together before the paint was dry! Slacken the strings and unscrew the bridge, pick the earth wire out from the body, clean it up and the rear of the bridge plate then move it to a new place and screw the bridge back on.
Check the other end at the jack socket and the general condition of the soldering etc, if its all good welcome to the hissy single coil pickup club, putting both pickups on full normally stops it, or buy a Stingray with a humbucker
I like bartolini pickups but they work best with active basses ime, I cant help with the wilkinsons, sorry.