It does fortunately. It's in the "axis tune" screen. Go to controls, Axes, click on the control that you want to adjust, the hit "axis tune" and you'll have a screen that gives you all the adjustments that LOMAC had (and more). I've toned down the gain of my controls a bit because as you said it's a sensitive beast.
As for the taking off, my advice is to turn on the "controls position" overlay (rctrl enter) and trim your joystick slightly forward before adding collective. It helped me a lot.
The trimming of Black Shark for non-ffb controls is rather unusual and I hope that they improve it in the first patch. If you've got the autopilot engaged without the flight director it's best to hold the trim key (t) down whenever adjusting attitude using the joystick. When you've got it right, release the trim key and reset the controls withing 0.5 seconds.
I personally prefer to fly with the flight director and do the trimming on my CH gear itself.