Please see the most recent updates in the "Where did the .com name go?" thread. Posts number 16 and 17.
I concur with your suggestion of the H-135. My go-to helicopter and I also use a Thrustmaster twist grip for control and TrackIR for maintaining visual awareness especially when landing in tight spots, like a Hospital Helipad.I've been using helicopters back since FS9 or earlier... Helicopters in MSFS are anyways more stable than the default Bell 206 we had since FS9
The trick is having your controls setup properly, about the response curve and sensitivities. It might be a bit too sensible at first.
I'd suggest you to train with the freeware H-135, which is certainly one of the easiest ones in MSFS.
The Cabri is quite uncontrollable for me, too light and too nervous. The fact that I use the twist axis of my joystick instead of a real set of rudder pedals doesn't help for sure...