The Pearly Gates is Alnico II (as is the Custom Custom, I think), so I reckon an AIV or AV neck pickup will sort out your muddiness problem.
I had a Rebel Yell bridge with an Abraxas neck which worked well enough, so I think RY and Mule would be good too. But as the guys have said above, if you want a bright neck pickup, Riff Raff is probably the way to go.