I have this exact combo in my bass.
The volume drop you're hearing is because of phase cancellation in the signals of the two pickups. This is NOT the same thing as two pickups influencing each other's electrical loading like happens in passive circuits, the Audere has a buffered preamp that doesn't allow that.
The signal provided by the two pickups has a different mix of frequencies taken from the string because they are sensing the string in two different places. This is the difference we hear between a neck pickup and a bridge pickup, even if the two pickups are identical save for their position.
In addition to that, there's a slight time lag between the moment a particular wave on the string passes over one pickup and the next. This means that the waveforms produced by the two pickups are slightly shifted relative to each other in time.
These two effects (especially the second) mean that when you combine the signal of the two pickups, there's a
comb filtering effect. Imagine it like a series of spaced out little frequency cuts.... like having a bunch of little EQ knobs spread across the spectrum and turning each of them down a bit.
The effect is the most noticeable to our ears in the midrange, since our ears are most sensitive there. This is why (in my opinion) blending both pickups on a Jazz bass gives such a great slap tone: the mids are scooped a bit in a pleasing way.
Long story short, this is an effect of blending two slightly time shifted signals. Doesn't matter how you blend those signals (run each pickup separately to its own identical amp.. stand equidistant from the two amps and you'll get the same comb filtering.. mixing in air or in electronics doesn't make a difference here) it'll still happen.
Take care, and enjoy those pickups and preamp. I am!