I think for me, my expectation of what a PJ could sound like is just never met - the bridge pickup seems overpowered by the Precision pickup, or like it's either on or off, or that it doesn't alter the sound in a way I find particularly usable.
Personally, I found my answer in a P/MM configuration. The bridge pickup is too far back to sound like a Ray, but it is beefy enough to keep pace with the P in parallel mode - and almost overwhelm it in series. I do have a singlecoil switching option in there to replicate a PJ, but I never really use it.
I tend to run it with a blend knob set about 75% towards the P, which adds enough bite and 'tightens' up the tone while still sounding like a Precision in the mix. YMMV etc, but for me, P/MM gives the sound that a PJ does in my head. Keep in mind I do play distorted, aggressive, fast music which no doubt plays a part in finding the bridge singlecoil a bit weedy.