The Ibanez S series guitars are relatively unusual because they're so thin, the wood has very little impact on the tone and while this would exclude some pickups, it also opens up other options.
C-Bomb
I'd certainly go with this rather than the A-Bomb in your guitar but I confess I have no direct experience of this particular model. In general the Nailbomb seems to be regarded here as a really good rhythm pickup but not that good with leads so as you specifically mention lead tones I would hesitate to suggest that this is your best option.
Holydiver
This is a very different beast to the C-Bomb. It's a very articulate pickup that takes an overdrive pedal really well but it's not as tight as the C-Bomb if that's what you need and it's not as aggressive. What you get with the Holydiver is essentially that 80s Metal tone with a bit of a modern twist to it. I found it quite a versatile pickup and unlike the Nailbomb, has arguably the best lead tone of any pickup in the contemporary range. As it's also AV instead of ceramic, you also get a richer tone.
Miracle Man
Personally, given the range of sounds you're after, I think this would be an excellent choice for you. It retains a lot of the feel of the Holydiver so it's rich, fluid and smooth but it has a bigger bottom end, more screaming highs, pinched harmonics are superb and the ceramic magnet makes it tighter. While the Holydiver is early to mid-eighties, the Miracle Man is late eighties and early nineties. I think this will get you into the Synyster Gates territory more easily than the Holydiver while retaining enough of the Holydiver to cover the other styles. While the ultimate tone isn't quite that of the Holydiver, it's surprisingly good for a ceramic pickup. It's excellent at rhythms and superb at leads, covering everything you say you want from your bridge pickup.
I'd put a Cold Sweat in the neck with a Miracle Man in the bridge but if you decided to use the Holydiver in the bridge instead, I'd use an Emerald in the neck as it's such a wonderful combination.