Momma also is not a fan of the movement, we had less movement in RTT. Air bagged it last week in hopes it would help, not much. Gonna try a leveling jack under tow hitch and see if that helps. Still thinking about annex room off back and would use adjustable tubing on corners to frame it in and maybe stabilize it.
The airbags are only going to help level the rear of a truck. The movement is transmitted through the bag to the suspension, may even be amplified by the bags. The only way to completely remove movement is to stabilize the chassis, as with the idea of using a hi-lift.
The movement is going to be very dependent on what modifications have been done to the rear suspension, if any. With progressive springs the initial spring movement is soft, this is the portion of the spring that will be flexing while you are in the bed portion of the Habitat. It could be a long road trying to dial in a suspension to reduce the movement.
Personally I'd work on blocking chassis movement, but I don't sense the movement you are describing, or the slight movement doesn't bother me, or the vehicle has different suspension.