I have a Les Paul Standard (mahogany body + neck, rosewood fretboard, and maple cap on body) that I play through a cranked Fender Pro Junior pushing a 2x12 cab with a V30 and a G12H30 in it. I have a Custom in the bridge position. I often use an OCD overdrive pedal in front of the amp. All that to say that I get a pretty thick, overdriven tone. I play hard rock and I like to shred.
I've had a nickel-covered PGn in the neck position before, but I felt it lacked clarity (it could get muddy). It wasn't as bad as the 59 I used to have in there, but it didn't cut through as much as I wanted it to. Maybe this was due to the nickel cover - I just don't know.
Would you recommend a Jazz (SH-2n), an uncovered PGn, or something totally different given my set-up and what I like to play?