As a fan of that sound, I spent some time (OK, a lot of time) trying to figure out what makes a 70s Jazz sound like it does, and besides pickups/pots there was body wood & type (the 'heavy' ash that Fender used around that time period), neck construction (not only wood type but a slightly 'deeper' profile than a modern neck plus bigger tuners), bridge pickup placement (70s Jazz has the bridge pup about 3/8" closer to the bridge than a 60s or 80s+ model) and (to a much lesser degree) type of paint/finish.
I ended up buying (of course) a 1977 Fender Jazz, reasonably priced owing to cosmetic issues plus no original pups/bridge/pots. I put in Nordstrand NJ4SV pickups and left the rest (CTS pots and cap were the same spec as original, it also had a Badass bridge) and the sound seems pretty authentic. Later I added a J-retro preamp.
Some time later I snagged a Squier VM Jazz to use as a backup, and swapped out a few things to try and get the sound closer to my '77 (btw, the feel of the neck is substantially different...width at the nut is the same but fretboard radius and that chunkiness on the older neck stand out). I had a set of Dimarzio Model Js and they got me closer. The Duncan Design pickups plus the maple body make it sound too bright, and the Js darken things up and kind of add body. But it didn't sound real close, something about the bridge pickup sound still was bothering me. Several part swaps later I think I'm as close as I'm gonna get with what I had lying around, which is:
-the orginal Duncan designed pickups
-an SX Jazz body (alder, but with the 70s bridge pickup position)
-control plate & electronics from the other Jazz
-Gotoh 201 bridge
-the Squier neck
The alder body and the Duncan pups kind of balance each other out--a little mellowing to the zingy pickups. The 70s bridge position, I think, is a big factor in the 'growl' that people talk about with 70s Jazz basses. I guess not all SX bodies fit well with Fender necks, but I must have had good luck there. If you're just looking to swap pickups the Model J or Fender vintage would be good to try out.