For reggae I tend to use my jazz basses because they have more lows. BTW It took me 15 yrs to find out the best reggae sound on a Jazz is to have the two pickups open at 70% unlike what you'll read sometimes on this forum where some will prescribe the use of the neck pickup with the tone rolled off. That set up is too honky and umdefined for reggae. (they usually don't play reggae themselves but assume they know).
I recently saw Aston Barrett live in Santa Cruz, in a very small room. I was just in front of his rig. I can tell you that he does NOT have his tone rolled off (he acutally uses an active Jazz Bass Deluxe those days). His tone comes from playing lightly by the neck at low volume, using a lot of bass cabs (2x15 and 2x410). Most of his eq controls on his 2 amps are straight. I actually knew that from his interviews but got to observe it first hand this time. His tone is like what you hear coming out of a subwoofer. I realized when listening to him that 95% of reggae bassist play way too loud and it gets really obnoxious.
I have two Jazz Basses, one is a 4 string with flats and one is a 5 string with rounds. They both sound really legit for live and studio. My PBass works nice for live reggae work because it is so punchy and it is sometimes what you need in a live situation.
In fact, I love the bass sound of Sublime's bassist and I believe he uses a PBass so it should not be ruled out.
Another PBass pickup to consider is the Aguilar 60's (I forgot the model). Aguilar truely makes legit vintage sounding pickups.