I'd say jump one way or another. I used a fine 73 PJ (was fretless, though) and despite trying loads of pickups, I could never get a PJ combo that "worked". Either one on its own was fine, but they were very different sounds and needed some amp tweaking, so it was never that useful in a gig. Eventually, I realized that dear Leo never intended the P to work with a J. Had the same experience with a Streamer Stage I.
These days I see them as two different things - a trad P with flats is a wonderful thing, but so is a J with rounds. Depends on the gig.
Sorry if that didn't help, but it has taken me 25 years to get there........
BB