Some of your air top end may be found in the sensitivity. Dial out some lows and mids and see if you still have girth and your highs.
Play with the EQ is ongoing. Current favorite is BASS at noon (give or take), MID at 2:00 or 3:00, HI at 1:00. Sensitivity is interesting -- I thought IN/OUT would behave like a simple boost, but that doesn't seem to be the case. OUT is a little rougher/more grindy (though grind might be a strong word) at all settings, IN a little smoother. Dialing it up indeed yields a harmonically richer sound, but going too high feels like it flattens the dynamics slightly. All the way down feels almost solid-state. In-between there's a fairly broad sweet-spot with varying degrees of bounce/harmonic richness/transient response. Got to play with this a lot more, though. There is plenty of BASS at noon, will try dialing it down and see how it goes.
fwiw, I think Monique sounds better through a dedicated power amp, and wrt the highs, wait to get into a band situation before you start chasing the air. On a related note I initially struggled with the dual coil pickups on one of my basses (my main bass is EMG PJ). I just didn't have the sizzle and air with the dual coils. But every gig recording I listened to had the bass just sound spot-on.
Don't have experience with a dedicated power amp, but agreed that I will have to see how I like things in a group context.
...Have you tried adjusting the treble and bass controls on your Dr. Bass cab?
No controls to adjust.

No tweeter, either, but the mid/high driver gets plenty bright and grindy with the Genz.
What room were you testing them in? Carpet/wood/tiles, brick/glass/drywall, etc.... that'll emphasise or mask certain sound qualities.
Typical, modest, early 21st century apartment living room with low carpet and thin drywall. Cab is less than 6" from the wall and, necessarily, played at relatively low volume at home.
It's a real surprise hearing the same gear sound so different in different venues.
Agreed! Some of my best "home sounds" didn't translate well at all live and at volume.
Agreeing with nostatic. My experience is that a dedicated power amp sounds better than an amp's power section. One major difference is the high end, which is much better in a dedicated power amp. It isn't as bright as my Mesa Buster up top, but Buster is a bright amp.
Are you saying that the Monique isn't as bright as the Buster, or that the top end on a certain, dedicated power amp isn't as bright as the Buster's?
...all of which illustrates how many design choices are made past the preamp in most integrated bass amps. Lots believe they're bypassing all the coloring and just getting the power amp, but that's almost never the case. There IS a lot of color and a lot of signal massage going on south of the preamp.
This I was not aware of. I thought that by plugging into the POWER AMP IN of the Genz that I'd be getting (probably) some hi-passing but nothing else. As for the high-end, *I think* that I noticed a similar roll-off with both micros as well as the Genz, but I spent much less time playing through them. Will double-check my impressions.
A friend just told me last night that he picked up a Peavey IPR 3000 (same you use, BurningSkies, if I recall). I rarely see him, but that might be worth arranging a borrow or meet-up for. Last I knew, he also had a very simple, one-tube pre (VERY bright sounding, as I recall). If he still has it, it might be interesting to play through it and Monique side-by-side, as well as to play both through the IPR and the Genz.
Thanks all for your thoughts -- feel free to chime in with more! I'm interested to hear folks' experiences with the Minne compared to other power amps (and will re-read previous posts there).
Will continue to play around with Monique -- still just getting to know it, really -- and report back when I have some more practical, beyond-the-living-room experience.
-Mark