The problem you are running into is something I have spent a lot of time chasing around and finally came to the conclusion that it is not really correctable with pickups or EQ. You can 'fake' it with EQ, or with a series switch, but you'll still be missing that base sonic information of uber low and strong fundamentals. And that's because that bass never vibrated in that way to begin with.
If you are trying to get a thick, growly sounding jazz instead of a poppy, thin one, it has a lot to do with the specific pieces of woods used for the bass, body thickness, and the neck pocket connection as well. To start with there are 2 different jazz bass body thicknesses out there, 1 5/8 and 1 3/4, go for the thicker one... unfortunately (?) the best thing to do is to start over... go to GC and play all the jazz basses in there unplugged... some will have a lower, more powerful resonant freq than the others, get one of those, put a nice set of pickups in it, and be done with it.
Not all jazz basses sound the same, I find that, possibly because of the pickup layout, Jazz basses tend to be much more different sounding from one to the other than P basses. The jazz pickups tell you more about the wood, so to speak.
I have 2 Jazz basses, one of them is bright, poppy, punchy, etc... really great for power trio kind of setup... it's almost like a baritone guitar. Very rad in that setup, I imagine it would be a jazz/fusion players dream. In a 2 guitar layout, it sonically collides with the deeper voiced guitar, and it can't cut through. Drummers look all confused, they can't make me out.
So I have another jazz bass... and that thing powers through like a freight train. It's like it was raised by P-basses, so it thinks it's a P-bass. Right on the verge of being muddy, but just poppy enough to pull it off. Maybe in a power trio, it's a little too boomy, but when dealing with several guitars, it is awesome.
The nature of the instruments doesn't change much with pickup swaps, I even used the same pickups in both, the truth is, you could tell before plugging them in, what they were about.
So don't throw money at the problem is what I would say... wait it out and find a jazz bass that has the natural properties you are looking for. Even if you improve things with this jazz bass, one that does "it" without any tweaking will always sound better - look for one of those.
Anyway, that's what my dozen or so Jazz basses I have been through have taught me about things. I think it gets a lot more important when there are more instruments, and you need to have your bass sitting in the right place in the mix... that's how I started thinking about this stuff at least. Good luck!
I have been having a bit of a problem with my Jazz bass, the sound is ridiculously thin. I have tried messing with the EQ on my head and it isnt really helping me much, also the tone control helps slightly but doesn't seem to add any low end.
I need a relatively thick bass tone, its not an amp or cab problem (Mesa Buster 200 and tour 410) as my peavey sounds huge and thick through my amp.
I have been thinking of getting an Audere and using that to send a thick signal with the Z mode setting that gives the most bass or getting a set of Dimarzio Model J's and wiring it in Series.
I really can't get another bass right now, I just need to use what I have now.
