Damn, idk how often it gets repeated that DC resistance does not mean pickup output, but people still don’t get it. Dimarzio Super Distortion for example measures only 11k but has more output than a JB at the same distance from the strings.
Taking a JB and just winding it to only 12k will not preserve the JB tone, simple as that. The best way to accomplish what you want is to move it further away from the strings. Or, find an alternative pickup of course, in which case you just need to trust someone - either the Duncan custom shop or elsewhere - to get where you want to go if you’re having something custom made.
The way I went about it was picking up various pickups for $40-60 used, trying them out, then selling them for $40-60 used. Cost me almost nothing but a little time with the soldering iron and I’ve had the chance to play every production line Duncan, dimarzio, and a few others. Nothing beats first hand experience no matter how many clips or people on the internet who give advice. Playing the pickups through your guitar and amps and room is the way to do it.
Also to the people who don’t like Dimarzios, no offense, but trying 2-3 of them doesn’t mean they are all bad. They make a wide range of stuff just like Duncan does. In particular Dimarzio makes some pickups with the “Dual Resonance” which some might love and others won’t. Essentially the two coils are wound mismatched on purpose in a humbucker, it retains hum cancelling but makes the pickup sort of sound in between a regular same-coils humbucker in parallel and one in series. Like the tiniest hint of a single coil brightness in there. Some describe it as “fizzy” (I’ve heard the Tone Zone described this way) while others describe it as “high clarity for its output.” Both descriptions are true. Also worth mentioning that dual resonance pickups sound different depending on which coil is closest to the bridge so that’s a factor as well. In short, if you’re not after that type of sound, which is a bit of a dimarzio specific tone, they do make same-coil humbuckers as well like the Super D, Breed or Double Whammy. I know I named two out of production models but they will still make them if you ask (and remember I said “buy used”).