You're assuming that "truly exceptional EBs" exist in the first place.
Manufacturing today is
astoundingly consistent and high in quality, even for a $200 bass guitar. As you noticed, the vast majority of EBs use the same designs, and it's pretty modular. I.e. I don't think there are a lot of physical differences between EBs in the first place.
But let's assume I'm wrong about that. The next issue is that there is no One Single Sweet Perfect Bass Tone.
The timbre(s) we like are all subjective... and extremely difficult to accurately recall after 30 seconds anyway.

One person can easily prefer "warmer" pickups, another "brighter" pickups, and both will insist that their favorite has "more clarity" or "sits better in the mix."
Further, the bass is going to sound different because of the context anyway. Even if every venue or studio you're in has excellent sound and great engineers, the timbre will be influenced based on the timbres, volume, placement etc of the other instruments, as well as the acoustic environment and choices of the engineer. As a result, I can't imagine there is one specific set of timbral differences that are simultaneously incredibly tiny nuances
, and are absolutely critical,
and are consistently superior in every context.
Even the most discerning listener would be utterly overwhelmed by that task.
So, what happens when we're overwhelmed with choices like that? Per
Barry Schwartz, one thing we do is exaggerate the minor differences. IMO this is why people obsess over tiny details that, on some level, they know will be ignored by the audience, missed by the other musicians, butchered by the engineer, and lost in the mix.
Thus, I recommend that you
don't sweat the small stuff. If you're getting paid, get a Fender, as that's what the people hiring you will expect; so it goes. Otherwise, find an instrument that sounds good and feels good when you play it, and don't worry about whether it is "exceptional."