I have a question:
What you described would seem to define the "Jazz sound" a lot.
Is doing it any other way (like passive volume/balance/tone) affect that "Jazz sound"?
How much?
OK, here's a reply maybe a bit long. Sorry in advance.
Leo designed "the simplest thing that might work" - it uses 3 pots, one capacitor, and it does something, It has real issues, though, so I do something quite a bit different.
The iconic Jazz sound (with the scoop and a nice, clinky high end) really only occurs when both pickups are on full - every other setting of the controls gives you something...else. The way I have my 2 pickup basses wired, I have a switch, that gives me 2 modes:
1) Neck only (like a P noically), with a tone control that varies the high (and mid) frequency content of that mode.
2) Both pickups, with a tone control that varies the high frequency content of that mode.
I don't have a bridge only mode, as I'd never use that (I play bass, I need all the modes to have decent and consistent low end). That could be done - it'd just take a 3 position switch.
The two tone circuits are different - the one on the second mode has a much lower value capacitor - with the tone "off" it's like I have hotter pickups - the peak is at a lower frequency, but it doesn't roll off all the mids and such like a stock Jazz tone circuit does. As the switch disconnects the tone control that's not in use, it doesn't have the issues that the original stack knob jazz had with control interaction.
This wiring also has a crossover for the bridge pickup - it isn't on at low frequencies, so both modes have the same low end of the neck only mode (a VVT wired jazz loses low end when you turn the bridge pickup volume up) and at mid frequencies, the "scoop" is not as deep as on a regular Jazz - a preference thing. As I'm using hum cancelling pickups, the whole thing is free of hum at any and all settings. While it sounds like this would have less sonic range than a VVT wiring, due to the independent tone controls, it actually has more usable sounds, they are all silent, and I can set up two sounds and switch between them with literally the flick of a switch. On a VVT setup, I'd be trying to turn 3 knobs at the same time, which doesn't happen fast and accurately in the same move.