Good answer, JTE.
That's pretty much my approach, too.
As I've said before, I believe that a better set of pickups for your bass is analogous to a better microphone for your singer.
Some vocalists require a mic with more midrange "hump", some sound better with a tubey-compressed treatment, some just need a "flatter" response mic.
I choose bass pickups the same way, to compliment or accent (or sometimes, DE-accentuate) what is going on with the bass in the first place, apparent even unamplified. My walnut body/rosewood neck Precision was too harsh with several of the pickup sets I had in it, but 62 RI Fenders were really civilized and well-balanced. And, no the bass does NOT sound like a vintage alder bodied/maple neck/rosewood fingerboard Precision. It's super-articulate, but the 62 P pickups sorta rounded-off the harsh edges.
And as to the strings...I believe that EVERY bass can be optimized to its BEST sound if you can just find the right type/tension/guage bass strings for it. I've had several basses that sounded very good with one kind of string, for example... my vintage P LOVES LaBalla halfrounds, but it sounded and felt like complete garbage with DR Sunbeams... which I put on a different bass and they sounded very good. But they weren't the right MATCH for that particular piece o' wood. Unfortunately, MOST bassists stick with one type/set/brand of strings through their continued succession of basses, and sometimes they match, but many times they come to the conclusion that "that bass SUCKS" bacause it didn't sound as good as all my other basses strung with the same sets of Rotos or flats. Too bad, it MIGHT not be the bass, LOL!! You just didn't try enough different strings!!
Also,too many times, discussions on TB center around what has the MOST or LEAST influence on a bass' sound, and tomewood is always thrown to the top or the bottom of the list. But I think it's a mis-interpretation of the question... the body/neck woods give a bass it's natural "timbre" and no pickups alone will completely erase that. It's inherent and overriding. However, pickups and strings are the EASIEST things to swap out, (especially strings) to get the biggest change to your overall sound.
It's all in how you think you're answering the question, whether you're ranking the components that are the most easily change-able (bang for the buck), or the structural components (body, neck, and to some extent, hardware) that are going to be constant and not refutable in their effects on the vibrations of the strings?
