Fender Japan Jaguar Bass 1962 Reissue (Modifications)

Hi everyone!

For recording purposes, I intend to use my Fender Jaguar Bass as my main bass and am considering modifying it to my wishes. The sound I'm after can pretty much be summed up in the following video, namely the third bass which is a vintage '61 Fender Jazz Bass (from 4:00):



Yes, I'm aware that the tone of that vintage Jazz Bass is the sum of its parts, meaning that the bass' body and individual parts together gives it its distinct sound. However, the Jaguar Bass I'm using does have Jazz Bass-inspired parts, most notably its neck and pickups. So I was wondering, and forgive me if this question might sound silly, would I be able to come close to achieving that sound by replacing the Jaguar's pickups with vintage-voiced Jazz pickups? Other modifications I have in mind are: replacing the wiring and shielding to reduce the Jaguar's noise; replacing the stock volume and tone knobs with special knobs that offer individual volume and tone controls per pickup; playing with flatwound strings.

So, fellow bassists! What are your thoughts? And has anyone here tried out something similar with their bass? I'm looking forward to your thoughts and suggestions. Thanks in advance!
Here is a picture of my Fender Jaguar Bass: