I'm a J bass fanboi. I have a PJ, too, but in my experience, nothing does P bass like a P bass, and it needn't cost a lot. If you want that sound, buy a used Squier and improve it. I know you are unlikely to get your money back if you upgrade extensively, but if you are selective (you only really need better pickups, pots and wiring), you should end up with something decent for less than £400. My Bitsa P is a Squier body and neck, with the basic Seymour Duncan P pickup (not worth getting the high output or vintage versions, imho), a Gotoh bridge, new pots, wiring and socket It cost me around £350 to build. With a set of knackered La Bellas, it does the job very convincingly.