Different points to be made. . .
Sorry... had to do it.
Seriously though, many good points already. Talkbass is a fantastic community. It can also be the bane of one's tonal existence (slight exaggeration, maybe). The problem with the tone you're chasing is that only you can "hear it" in your head.
I have found "my" tone in a used Valenti after having owned Fodera, Elrick, Sadowsky, etc... My tonal adjustments consist of rolling the passive tone knob up or down occasionally.
One thing I haven't seen addressed yet, is that the Music Man/P bass tone may not be for you. You may prefer a Jazz once you get it into the mix, or possibly a Smith, etc... It's my opinion that if you are using a quality in-ear system, what you should be getting from the board is a flat representation of what your bass sounds like. That's an excellent place to start. If you can't get it sounding good in your ears, it may be that the bass isn't for you, or that your technique takes work (no shame in that, we can ALL use work on technique).
The amplification thing throws another wrench into the mix. I actually got some very good responsive in-ears and bagged my stage rig at church (LMII and Epifani UL-210S1). Why? Because the "pure," flat tone of my bass running through a Countryman DI and into the board with no EQ,
is the tone I hear in my head.
I spent years playing 12's because I love low end. I was never satisfied because they lacked the definition I wanted. So, I moved to 10's. Voila. It just takes time and experimentation.
I believe most of this is going to come down to some searching, and possibly some cash expended on your part to figure out. I personally believe the 100% is possible. I'm there with my fretted 5. I now have to get there with a fretless, but my experience over the years will help me to have ruled out a large number of basses, pickups, etc... but that's another story. Now, my amp doesn't sound as "pure" as the in-ears. To get there, I'd probably have to shell out for some reference monitor-esque cabinets, a pre, etc... and I don't gig enough to justify it.
I'm sure that wasn't helpful, but at least you killed a few minutes reading.