Another important thing that I missed:
I often use distorted chord inversions with 3 (or even 4) voices; and I want a pickup that let me hear those voices as clear as possible!
I owned a Gibson Les Paul Standard 2012 with Burstbuckers Pro. They sound much better (for me) than the pups on this Less+ but neither of them is able to separate well all the voices of a distorted chord. My fear with the A-Bomb is that it confuses the chord voices too (because it has a very rich and hairy sound)!
The Burstbucker Pros are good pickups.
For note separation and clarity, you have to look at your tone / amp settings as well as your pickups because the mud may originate somewhere else in the signal chain.
If you want maximum clarity and note separation -even under obscene amounts of gain- the Rebel Yell will do this. It also sounds great with heavy strings and low tunings. The pickup is tight, bright, and clear. It takes tonnes of gain but may be too thin and upper mid focused for your guitar. It has a similar voice to a Burstbucker Pro but with a higher and tighter low end.
The A-Bomb does have clarity and note separation but it is thicker sounding than the Rebel Yell. It may be a great match for a thinner sounding instrument with less low end. I 'hear' that it doesn't handle drop tuning as well but I can't confirm this as I have yet to drop tune it.
The Juggernaut Bridge is even more powerful than the A-Bomb and it sounds thick, but in a different way. BKP says the twin screws will emphasize clarity and give slightly higher output than the twin bolts I have in my Juggerbridge.
Based on what you've been saying, I'm actually leaning towards suggesting a Juggernaught Bridge so that you can do clean as well as rhythm and lead for metal. If you can EQ your setup to emphasize the top end, it should serve you well. If you're worried about complex chord voicings, just listen to Periphery's music; It's essentially a bunch of bad jazz chords lool. Just be sure to get the twin screws instead of the bolts, even if the bolts look better.