By now, I've enjoyed a few sessions with Monique. My extremely subjective thoughts/review of sorts:
This girl is thunderously thick. With fantastic proportions... thick curves in all the right places, trim and svelte where it counts, and not a bit of flab. Soft and supple to the touch, but there's serious muscle in there. Ask her for a kick in the low end and/or a punch in the gut and she could *really* hurt you.
Soft, gentle and sweet on the surface. On all counts a lady. But get her riled up, angry, or just overly exited and she can knock you on your hindquarters.
Her natural character ranges... syrupy sweet and comforting, to fun and friendly, to commanding presence, to a little bit naughty. Turn her knobs just right and she'll even hint at getting dirty. But not a lot... won't get nasty without some prompting. But talk dirty to her, and you may be in for a surprise... she really digs it. Lets totally loose on it, and gives it right back better than she's getting it. Be prepared to get tossed around like a rag doll, and maybe mend some broken furniture.
And it doesn't matter whether she's playing sweet and soft, or hard and wild... she's really hard to let go of. You wanna keep going till you just can't anymore. Whatta gal!
OK, enough with the anthropomorphic silliness.

What I was after was tubey thickness/richness and feel. And that's exactly what I got. Lots of it. Can easily dial up more juicy low end than ever needed, while somehow never getting flabby. The thick isn't just in the bottom either, it goes all the way up.
The sensitivity knob is a combo of "how much tube feel" and "how much Monique". Dialed all the way down there is still plenty of tube feel and harmonics, but it's a lighter/tighter dose. You're very much in control. Turned all the way up, the feel is really deep and springy, and the harmonics thicker and heavier. She's on top of things, having her way with your signal.
The EQ knobs are interesting. Just cranking the knobs around, it is obvious what they do but they seem to be on the subtle side. Start in the middle with the lows and crank them all the way down... you still hear plenty of lows. They're just "out of the way" of the other frequencies. Back to the middle it doesn't seem a lot more, but they are more even with the rest. Bump them all the way up and they get huge, yet not out of control or covering up other frequencies. The other knobs work pretty much the same way. While the knob twirling by itself seems subtle, the range of results somehow isn't. Turning the knobs does what you expect to the tone, but you still everything clear as a bell. (Is that what folks mean by "3D" sound? Dial down highs, and they just move farther away, and to the side. Still there, still clear, just out of the way.) Strangely foolproof, while still letting me get where I want to go. I usually have an innate ability to make anything sound awful, if I put my mind to it. But Monique seems to sound good no matter what I try.
So... yeah. Pretty much what everybody else said already. Aka "Monique rocks".
But so far it's all been only in the bedroom... I have yet to turn her loose in a band context. Both bands were off for a couple weekends. Looking forward to this coming weekend, to give her a go for real.