Squier 60s Classic Vibe - Chet Baker solo

And again something different. I was wondering..
I'm not too familiar with all of the jazz bass pickups out there, but I'm trying to get as close to the 60's sound as I can possibly can, by replacing my standard Fender Alnico pickups. And yes, I know that the way of playing also affects the sound you create. That's why I've got a few in mind, which I love.. based on comparisons that is. Those include:
- Bartolini B-Axis set
- Fender CS60 set
- Fender '62 handwounded set
Anyone familiar with any of these (or any warm/authentic sounding) pickups? Please leave a comment with your recommendation and I'll be sure to check 'em out! Thanks a lot in advance!
By the way, this is only a slightly modified Squier 60's Classic Vibe series jazz bass. As you can see, I added a thumb block and a pickup cover to it. I just coudn't resist. In the near future, I'll have this badbass reliced, as well as the new pickups installed. Can't wait to get this baby back in it's new body.
I ran the bass straight into my Clarett interface with a very light compression for dynamic control, by using the Slate Digital VMR.