Thanks all for the replies so far. Keep 'em coming...
I've played my Precision for so long, that's the "sound" I hear in my head when I play bass. This Jazz I recently picked up just doesn't sound anyway near that. I know, I know... it's a Jazz bass.
Actually, I think my two main complaints are (1) the sound just doesn't seem to have the balls and punch that my Precision has... sort of a tame limp sound. (2) The string balance is noticeably off, with the A & D strings lower in volume than the E & G strings. This Jazz has the 7" radius so there is a height difference over the pickups... not sure if that's the reason for this output difference.
This instrument is set up correctly... I've done my own setups for years and know what I'm doing. The strings are just fine... Chromes. Which has lead me to consider changing out the pickups.
I am a "leave it alone and play it" sort of person. I don't spend any time trying out different components.... just not my thing. But this Jazz needs help, and because this feels so good and could easily become my main player, I'm going to tinker a bit with this one.
The suggestion of Dimarzio J's is a good one. Thanks. Someone also strongly suggested Nortstrand split stacks with the raised center poles. Anyone care to chime in...