Full shred set, most definitely.
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You'll not be happy with them until you boost the bass at your amp a bit. Doing this makes them thump and be super tight as the same time.
Like the JB and other “bright” higher output pickups, the Full Shed doesn’t present as all that bright until the tone starts to saturate. It isn’t particularly bright at the cleaner end of the spectrum compared to a pickup with less wire which appears more in line with the original poster’s needs.
Good cleans and overdrives, some distortion tones.
The Full Shred is nothing more than a Seymour Duncan Custom with an A5 magnet and two screw coils populated with Allen bolts. Between the two, the Custom is the brighter pickup; much brighter than the Full Shred when played clean or crunchy.
Now if the aim is a hotter-than-vintage Seymour Duncan with an aggressive top end, the Perpetual Burn is a better choice for the amount of gain the OP is describing, though I will still point to the leaner, lower-output Screamin’ Demon. The Custom (and its variants), the Perpetual Burn, and the Screamin’ Demon are all 43AWG.