I would suggest this as a quick test to see if the problem is with the new pot or how it's wired: Disconnect both hot wires from the lugs of the bridge pot and connect them together. In other words, you're bypassing the pot completely and running the pickup output directly to the 3-way switch. Leave the ground wires connected to the back of the pot and be sure they are making solid connection there. You also need to have that third "unused" lug grounded to the pot. See how the guitar sounds once you've got that all checked out.

I would also suggest checking to make sure your three ground connections on the 3-way are all solid/intact.

Side comment: Gotta admit I don't like how long the ground wire runs are on this guitar, which I think are more prone to developing problems. The 3-way on the Wildkat is a l-o-o-o-n-n-n-g-g way from the two volumes and the tone pot. Much prefer the usual Gibson practice of running ground connections directly between the backs of the pots rather than up through the 3-way. Example HERE, though it's for humbuckers and no master volume.