I think that more than the electronics, what you are hearing is the unusual pickup location, which is closer to the bridge. I've had a love/hate relationship with the 5-24s, but ultimately, I love them.They do sound great in the mix, both live and recording, although generally are not a crowd-pleasers by themselves. I've learn to love the sound, especially because it's so different from a Fender sound.
I have also thought about putting some Nordstrand Big Splits to liven the sound and make them more aggressive, but like i said, I have learned to love the sound and don't think it's worth changing anything. Every time I hear somebody playing one, I think to myself how amazing they sound.
I always boost the lows at least 1/4 of a turn, and tend to favor the neck pickup. This sounds huge. I also boost the treble a bit if I want to hear myself better (I wear earplugs when playing).
All this said, I would think you could also benefit from a 3-band EQ, or even a graphic EQ, so you can bump a little on those frequencies you are missing that the onboard preamp doesn't give you.
I also have a love/hate relationship with the Sadowsky preamp. I have an onboard one that I use with other basses, and man, it sound so round and sweet, but it does take away some frequencies that I miss from the natural sound of the bass, most likely some mids. . .
All in all, I do prefer the sound of a Lakland 55-94, for example, but the playability of the Sadowsky (and the 34") made it a winner for me.
And in conclusion, I don't see anything wrong with changing the pickups and/or the preamp. That might do it for you, but remember that the signature sound of that bass is baked-in with the pickups' location.