Is there any chance the closed loop mode with linkage activates the pot on the wrong side? Leading the servo to conpensate, on the wrong side (aggravating the difference between the setpoint and the current position, instead of actually correcting)?
When you say 1mm dead spot, is that at the tip of the servo arm? If so what is the lenght of the arm? It seems ok that the arm moves 1mm on such a large scale before any movement is made as to avoid oscillation (overreacting of the controls)