Update: My desire for "P-in-J" may not have been entirely literal. I didn't know (and perhaps still don't know) exactly what I'm looking for. What I'm looking for is a way to give my J bass some of the presence of my Mustang during gigs. My first thought was "P-Bass", and I even have a p-bass body sitting around my closet, but the J-neck isn't compatible. The Tagima has a very wide neck pocket. But P isn't the only possibility. It's been an issue with long-scale basses in general that I've been having trouble getting my sound, which is annoying, because I almost always practice on a long scale, and I'm a big guy. I had similar issues on an Ibanez RB820, which has Music Man-style pickup placement and tons of mids. I can get much closer on the Jazz.
I know that all this is largely a matter of string tension. On a longer scale bass, I don't get the splat followed by the fundamental. The sound is more uniform. I've tried foam mutes, black nylon strings, preamps, etc. I have managed to get the JB to the point where it's tolerable, but the pickups are polite. If this bass didn't play so well, I'd just let it be.
Additionally, I discussed this with my advisor/teenage daughter, and we came to the conclusion that there are only a few aesthetically-correct replacement pickups for a custard-colored punk rock Jazz Bass. 1) Black Model J with black pole pieces, 2) EMGs, 3) overt cheapos (but I already got em) 4) I'm touched by Bartolini's efforts to market themselves to punk rockers as indestructible. That leaves me with a 90% chance that I'll go for the Model Js and switch out my pots for 500s. 10% chance that I'll go for EMGs even though they're the opposite of what I say I'm looking for. Maybe I just need a bunch of highs for the click.