Hmmm... To the extent it is in the voicing or the response of the amp or speaker cab, then it should be apparent regardless of the input device. That is, you should get it with a piezo, a mic, or any other transducer. I wonder how much of the objectionable sound you hear is just a function of the amp. Hard to say from here.
But what if, as I wondered aloud in my previous post, the slightly resonant frequency of the pickup/bass/setup in question matched the slightly resonant frequency of the amp setup when set flat? Wouldn't this likely produce a resonant frequency hump that might in some ways sound waterfowlesque to the imaginative listener? If so, it's not a big deal at all if the player knew which frequencies to roll back to tame it. Or maybe I should just quit while I'm behind.
EDIT: I see we cross posted, and that you've already answered this. Time for this hayseed boy to shut up and go practice!
I've never been a fan of the idea of variable input impedance. It's a parameter that alters frequency response in a way that's highly dependent on the device plugged into it. I much prefer optimization of input impedance followed by a really good tone shaping circuit (I prefer parametric ones, as on the EA amps). Optimization is what that switch does for different condenser mics that Chris mentioned. IMO, a variable impedance knob approaches (not "is," but "approaches") electronic snake-oil in many cases.
I use a Rev Solo 2, fdeck's pre-amp/HPF, an EA iamp200, and a Wizzy 12. No quacking, no honking. I can produce honking if I throw on a BassMax plugged into a less desirable rig. Just my experience.
Understood and appreciated.