Well stated Mr. Wind.
The "specification" that is most important is the Input Sensitivity of your amp. As you said, the (wonderful) IP's are asking for .775 volts RMS. So are a whole lot of other good amps. Monique as she sits today is optimized for that Input Sensitivity. She is also optimized for a 10K input impedance from the Line Out and a 600 ohm impedance from the Balanced XLR Out.
For you and me in the Bass World, the impedance can and will make a difference, but not as much as the Input Sensitivity.
Warning! Now leaving the Bass World for that of the geekazoid. My advice is not to read any more of this because it will not help you play any better.
A generalization I can make about impedance matching connections is that 1:1 matching (such as 10K to 10K or 600 ohms to 600 ohms) is best. By "best" I mean that stuff gets transferred across the connection like we want it to. "Stuff" includes the audio and the playing characteristics.
To continue the connection generalization, if there has to be a mismatch (like your ~10K passive bass pickup to a 1Meg amp input) it is best to go from low (10K) to high impedance (1Meg). This provides more current, which is what does the work. This is why piezo pickups (extremely high impedance and low RMS voltage out) need buffers to sound as good as they can into a normal amp. Piezos (un-buffered) go from HI to LOW impedance, so there is less current to work with - stuff gets lost.
Your example of parallel/series output impedances sounds good on paper, and is entirely reasonable, but that isn't how it actually works. The description as to why it doesn't work is boring beyond belief, so I will spare you.
In all this, I apologize to all the EE folk out there for my generalizations of something that you spent semesters learning in so much more detail.
Let's just make music.
Balancing doesn't typically put the two inputs in series in the way you're thinking, but there are a few different ways it can be implemented. The impedance will also change depending on whether you use a balanced or unbalanced connection. What specific amp do you have?