I'm going to be a contrarian: I have a RA Mouse. Often cited as the "closest" to an upright. Used it for jazz for awhile. Obsessed over tone. I mean obsessed. Researched, read posts here, bought compression and reverb pedals. A/B'd against jazz recording loops until my tone was pretty darn close to the tone I was hearing on the record. Let's just say, OCD to the max.
My jazz mates, including pro pianist — don't notice any difference. Drummer says, " I know you say this is supposed to sound like an upright, but I just don't hear it."
So, I bring a (pick one) fretted bass to the next rehearsal — "oh, that sounds nice — good definition."
So, after all the obsession — have largely settled on a fretless Precision with flats for my jazz stuff.
Point being: you're right — mostly no one but you hears or notices.
Are you telling us playing in tune and on time is more important for supporting a band than chasing tone?