This is going to sound like I'm just plucking out the most thoughtless answer here, but seriously, the Full Shred Bridge. I have a set in a Les Paul and they work beautifully for balancing out that guitar in D Standard with slightly heavier strings. I can't handle .012s, but I do use a set of .0105-.054 (IIRC a standard .012 set ends with a .056) and the Full Shreds keep that guitar sounding clear enough for high gain but still fairly thick as Les Paul should. (I can't say I've ever tried them for Drop C, because any time I tune lower than C# I just go to active pickups or a 7-string.)
I have another LP which is identical in build but with a Jazz and Custom 5 set, using the same strings but for Eb Standard. The Jazz and Full Shred Neck are the same pickup, just with different pole pieces; the Full Shred Bridge is a Custom 5 with different pole pieces. When both guitars are tuned the same (either D Standard or Eb Standard) you can't really tell the difference between the two pickup sets. The Jazz/Custom 5 combination is just a tiny bit heavier in bass, but it's a small difference. The way I think of it is the Full Shred set is those two pickups (Jn/C5) just optimised for slightly lower tunings; by not having quite as much bass they stay just a little bit clearer as you tune lower. It actually baffles me that they're called 'Full Shred' when to my mind they're most ideal as slow, chugging rhythm pickups for muddy guitars.
So, you can look up what people like to put with a Jazz neck and know that anything that blends with the Jazz well will also match with the Full Shred, since they are 99% the same. As I said, my pick is the Full Shred Bridge, which obviously is as close a match as you can get. The Custom 5 also does well with the Jazz/Full Shred if you want just a little bit more bass, or the Custom works great if you like the Full Shred tone balance but want more output overall. (Though the Full Shred Bridge isn't that far behind in output; I think Seymour Duncan are very wrong to market it as a 'medium' pickup.)
I don't know why anyone would put the Invader with a Full Shred unless they only looked at the pole pieces and figured they look close visually. Tonally they are total opposites and the Invader bridge massively overpowers the FS neck in output. For reference, I do have an Invader, I like it a lot but I've never found a neck pickup that matches well with it, including the Invader Neck. Right now I have it paired with a Distortion and it's still a total mismatch in output and tone. I'd also never put an Invader in a Les Paul, it's really matched for thin-sounding guitars.
Some people will suggest the JB, I'm sure; not a fan myself, especially with the Jazz/Full Shred where I've found the more evenly-EQd and fractionally less hot Custom 5/Full Shred bridge is a better match. JBs overpower them.