PJ is okay... but a P/Hum is scads better.
Jazz pickups usually don't have enough oomph to keep up with the P. In a PJ, the Jazz ends up being more of a spice to the P -- it's present but it's not the main thing you're tasting.
Humbuckers, however, are better suited to keep up with the P. They can even be soloed and don't sound thin and nasally. Nordstrand's Big Split, Big Single, Fat Stack and sooooooo many more compliment a P brilliantly.
I completely agree--J pickups don't match well with a P. Which is why I prefer a J with the P. I like the J because you can dial in a little to adjust definition without losing what makes the P special. If the bridge is dominant (or even 50/50) it's not P/J tone IMO.
I've been lusting for a P/P (reverse?) for some time now for exactly this reason...