The crawler bridge could do for the "sweet cleans and rich, fat and growling distorted tones", but I think it needs a rather bright guitar. The ABomb will certainly have enough clarity and punch and I don't imagine it could become muddy at all (this pup can retain clarity and definition at insane gain levels), but I don't think it will give you the "sweet cleans" nor the "fat" distorted tones, it's rather on the tight, bitey, cutting, "chainsaw massacre" side.
Both have the definition, articulation and note separation that seem to be the BKP signature, both are rather organic and very "alive", with the Crawer being very warm, a little compressed (in a good way) with a good "oomph" factor, and having a definite vintage twist, and the ABomb being much more open, dynamic and agressive, and more modern sounding - while still being able to give more classic rock tones when you roll of the volume. Both are great pickups when they find the appropriate host guitar, but I don't think I'd be that happy if I swapped them (the Crawler being on a bright going-thru maple neck / maple side / rosewood japanese Vox and the ABomb on a rather dark and full-sounding SG).
Given your guitar's description and your tone requirement, I think the Crawler would work better than the ABomb for you. I didn't try any of the other pups you listed.