None are doing everything you want but all are excellent at part of it. I'll try to pick out the words from your original post that I think might fit with each pickup:
Miracle Man - 'huge', 'lots of intestinal fortitude', 'hot and high output humbucker', 'thick', 'punchy', 'chunky', 'beefy', 'warm', 'bottom end to be wide and fat but clear', 'high end to soar and not scream', 'far away from a "thin" sound', 'great string to string separation', 'Thickness, punch, heat, warmth, "balls," and clarity'
A-Bomb - 'huge', 'lots of intestinal fortitude', 'hot and high output humbucker', 'thick, raw, punchy, chunky, beefy, warm', 'fat but clear', 'far away from a "thin" sound', 'great string to string separation', 'Thickness, punch, heat, warmth, "balls," and clarity'
Cold Sweat - 'lots of intestinal fortitude', 'hot and high output humbucker', 'punchy', 'clear', 'high end to soar and not scream', 'away from a "thin" sound', 'great string to string separation', 'punch, heat, "balls," and clarity'
The only thing I'd add is that the woods in the guitar will be crucial in choosing your pickup. The Cold Sweat is quite bright so is better suited to Les Paul style guitars. The A-Bomb is also VERY aggressive and hairy sounding and the wrong woods will just highlight that. I tried one in a maple neck-thru with alder wings and it was really awful but I may be trying it again in the New Year in an all mahogany Les Paul copy. The Miracle Man works well in many things unless the guitar is very dark.
Of the neck pickups you listed, the Cold Sweat is the one that is certainly the closest to your requirements, though your description also describes the Emerald very well. Don't be fooled by the EQ charts as they only relate to the bridge version. The neck Emerald is everything you want. It's perhaps a little brighter than the Cold Sweat but certainly not a bright pickup and it has a sweeter lead tone thanks to the AIV magnet.
I would describe my tastes in tone as quite similar to yours and I've also tried all of these pickups before and I'd take the Miracle Man again in a heartbeat. For the neck, I prefer the Emerald over the Cold Sweat neck but it's a bloody close call between the two of them. You can't really lose with either of them.