My thoughts exactly. I can use my 44-94 style Carlo for nearly everything, but when I want a passive P-bass sound I pick up my much-modded MIM P-bass. It nails the sound the Carlocan't and has a great shallow neck.
The good news is that the P-bass formula is dead simple so it doesn't take much to get a great P-bass tone. I'd love to have a Lakie and I think all of us here will point you in that direction, but the truth is that a MIM P-bass and a good pickup will get you 99.9.% of the dream P-bass tone. Heck, a Squire and a good pickup will get you 95% of the way there.
Are you currently playing with a backup? A passive P-bass is great to have around on a gig for those times when the tone is required. Further, as a backup instrument, it might not be perfect for every song but there's almost nothing to go wrong with it and you'll never sound terrible on a P-bass.