I've got a drawer full of old 80s JBs (mostly JBJs), and while most are around that typical 16.4k mark, a couple are in the upper 15s and one is a total outlier at 17.1k. I don't believe the roughcast (old) vs polished (modern) magnet causes much audible difference in a JB - I've tested this swapped them around and not found any results that I could say definitively weren't caused by minor height discrepancies (half a mm can cause a pretty noticeable difference in tone and feel).
All that said, if you want to get an old JBJ I'd advise seeking out one with a DC in that upper 15k range since they'll naturally have a clearer and tighter sound. Also make sure it's not a F-spaced as a wide-spaced pickup on a Gibson string spacing will cut a fair bit of output from your lowest and highest string.
For what you're describing, I'd recommend a Distortion. It's the same wind as a JB but with a ceramic magnet - gives you tighter low end, less mid honk, and more pick definition. Oh, and lots more output too.
Bare Knuckle-wise, the Holy Diver used to be the closest to a JB since it was the only BKP wound with 44-gauge wire (crucial to the JB sound, IMO), but the newer Silo bridge model also uses 44AWG and has symmetrically wound coils like the JB does (again, pretty crucial to the JB sound). The Silo's scatterwound 15.7k gives you more clarity and tighter low end than a JB, and having double-row pole screws gives you a bit of thickness. I think it's a great pickup that'd serve you well, given your wishlist.
Now, if you want to step outside the 44AWG bubble, there's a huge list to try. I'm sure others will give you plenty of suggestions
