The restrictions for flying with front doors off are due to possible controllability problems when the C of G is too far aft, or where aircraft response will not always follow a predictable pattern for a given cyclic input. In addition, the back doors, with the original handle design, tended to blow open in flight, and the changed airflow over the static ports may cause the altimeter/ASI to misread slightly.
In other words, the anticipated rate of speed increase or decrease with movement of the cyclic forward or backward may not be achieved with doors off, due to disturbed airflow. It is a carry-over from early versions of the 206A which, when flown at very light weight with the doors off, had negative static stability, meaning that the fuselage did not try to return to its original position after a disturbance (helicopters are normally statically stable). For example, if you settled down at 60 KIAS, then accelerated to and held 70 KIAS, the longitudinal cyclic position would actually be slightly aft of the 60 KIAS position. Because of this, the problem got called Cyclic Stick Reversal, but there has not been a situation where you had to push the stick forward to make the nose go up. The negative static stability may arise from the effect of airflow on the horizontal stabiliser.
As the 206 series increased in empty weight, or if you flew it at something other than empty with nearly no fuel, the problem went away, but it stays in the supplement as a restriction.
Does that help?
Phil