P bass for reggae is largely a myth, IMO, perpetuated by people that haven't really done it or even really A/B'd the different tones in a J and a P but it seems like you already know that....
*snip*
shifting the balance to the neck pickup...
What exactly do you mean by "is largely a myth"?
Blending to the neck pick-up on a J tonally is very close to P-bass style sound, so i don't understand both those statements being valid.
Personally, my best reggae tone comes from a P/J with flats, rolled all the way to the neck (read as "P-bass") through an all tube pre-amp into a monster solid state set-up. This combo gives me the deep deep lows, but doesn't get loose while still retaining a very warm tone.
As other's have mentioned, technique counts for quite a bit. You can get a reggae style sound on any bass by playing with my thumb and muting properly.