I can think of two, great P/J's, but both are built around Jazz specs, so for some, that could be a non-starter. Still they're worth mentioning.
1. Fender Aerodyne Jazz...specifically, the first-generation.
Excellent build quality from Fender-Japan. The pickups may not be for everyone, but I've found that adding D'Addario Chromes gives it a bit more
"thump". Otherwise, the pickups can be switched out to fit one's tastes. Changing the pots can be a little trickier, given the narrow rear-routing.
Finding a used one isn't difficult and the quality gives a lot of bang for the buck, even if one wants to mod or upgrade it.
(e.g.: I'm currently seeing four on Guitar Center's used database, all for around $700.)
2. Fender Reggie Hamilton Jazz.
An interesting mix of American and Mexican parts. One good thing, though, was that they were built after Fender had executed their across-the-board quality control bump in 2008.
I had a Mighty Mite J-body re-routed to mimic that pickup placement and it was a fantastic decision. If one is thinking of turning a J/J into a P/J, I highly recommend getting a WD Music Reggie guard to use as a template.
As for the preamp, I must mention this; while it can switch to passive mode, it doesn't have any tone control, just a pickup blend. However, there's a fair amount of room inside for an upgrade. Basically, it's built much like the Fender Deluxe Active basses from around the same time, complete with a screw-down battery cover on the back.