oh i see what you're saying, the air norton too bass heavy to match with anything but the tone zone. that's interesting the eq chart for the air norton is B:6.5/M:7/T:5 while the breed neck is 7.5/7.5/5, but I guess eq isn't everything.
I wish I could just buy the air norton to try, but then I have to drill out the holes in the feet to direct mount it, then I can't exchange it, and it makes it difficult to resale....
Yeah the Breed has a lot of bass, but it's much more controlled and the pickup as a whole is much more articulate, so it doesn't show as much. The AN has basically zero treble in practice, so the low mids and bass are a lot more apparent (and the attack a lot less), really the only place I'd even consider using it myself is in an archtop or semi where it's the only pickup.
If you've played basically any Ibby RG Prestige in the past 6-7 years, they mostly have a TZ/AN setup. They're pretty even tonally (the basswood ones at least), leaning a touch to bright, but that setup makes them super grindy and crunchy, great for modern rock. Since both pickups have a ton of low end, you can set your amp up in a way that'll work with both pretty well. In a less balanced setup, you need to decide in advance which tones you're gonna use for the neck pickup and which are for the bridge pickup and any splits - otherwise your neck pickup is gonna be muddy and inaudible unless you overpower the rest of the band with volume, or the bridge pickup is gonna be as sharp as Nippon steel folded over a thousand times.
I don't like the Air Norton because of its lack of pick attack, but it may be exactly what you are looking for. To me it is a mud bomb that doesn't even feel like playing a guitar when I use a lot of gain. More like a synthesizer. There is some kind of strange "emptiness" to the Breed neck that I never liked too. I do like the Liquifire though.
The synth description is pretty accurate. The JP pickups have more of a midrange focus and less bass compared to the AN so they play a bit better under gain IMO, but they seem pretty flat and characterless - which makes sense, the JP sound is basically all Mesa Mark and the pickup just needs to give it the right kind of push. I'm a H&K player and their amps are really transparent, so I need my guitars to have a lot of color and character to make up for it. I like the Suhr pickups in my Strandberg and the Kiesel Lithiums in my CL6 the most, with the Dimarzio Fusion Edge set in my RGR Prestige (ash body, rather than basswood) being a close third (though they're pretty transparent themselves - the guitar has a ton of color even acoustically, which makes up for it). I find that Marshall and Vox amps (and those based on them - my Grandmeister is basically a very angry multi-channel AC30 tonally) react similarly and want some character from the guitar, but Fenders, Mesas, and stuff like the 5150 and 6505 are a lot friendlier to a more transparent or flat setup.
What might work for you is a magnet swap - an A4 would give you a really sweet midrange (probably my favorite magnet for more vintage-vibey applications personally) and cut the treble a bit while staying defined; something like an A2 would give you a ton of low-mids and a pretty noticeable treble and attack drop.